WORKS  OF  PROF.  S.  E.  TILLMAN 

PUBLISHED    BY 

JOHN  WILEY  &  SONS. 


Descriptive  General  Chemistry. 

A   Text-book    for    Short    Course.      8vo,   cloth, 

$3.00,  net. 

Elementary   Lessons  in   Heat. 

Second    edition,    revised    and    enlarged.       8vo, 
Cloth,  $1.50,  net. 

A  Text-book  of  Important  Minerals  and  Rocks. 

With  Tables  for  the  Determination  of  Minerals. 
8vo,  cloth,  186  pages.    $2.00,  net. 


ELEMENTARY  LESSONS 


IN 


HEAT. 


BY 

S.    E.    TILLMAN, 

PROFESSOR  OF  CHEMISTRY.   ITNITED  STATES  MILITARY  ACADEMY. 


FOURTH  EDITION. 

REVISED     AND     ENLARGED.",     \  l\ » 
FIRST   THOUSAND 


NEW   YORK: 

JOHN    WILEY    &   SONS. 
LONDON  •    CHAPMAN   &   HALL,    LIMITED. 
1911 


COPYRIGHT,  1892,  1901 , 1907, 

BY 

8.  B.  TILLMAN. 


THE  SCIENTIFIC  PRESS 
lERT   DRUMMOND   AND   COMPANY 
BROOKLYN,    N.   Y. 


PREFACE   TO   THIRD   EDITION. 


THE  preface  to  the  first  edition  of  this  book  read  as  follows: 

"  These  lessons  have  been  prepared  to  meet  the  necessities  of  a 
very  short  course  of  study  at  the  Military  Academy  in  this  branch 
of  physics,  a  course  so  short  that  it  can  command  for  study  and 
recitation  only  about  seventy  hours  from  the  cadets. 

"  In  selecting  the  material,  I  have  been  guided  by  the  consider- 
ation of  what  is  applicable  to  the  subsequent  courses  of  study  at  the 
Academy  and  also  of  what  is  essential  and  most  useful  for  the  stu- 
dent to  know.  In  the  arrangement  I  have  kept  in  view  facility  of 
acquirement  and  thorough  understanding,  and,  accordingly,  the 
logical  connection  of  the  facts  and  principles  set  forth. 

"In  the  exposition  of  the  subjects  treated,  I  have  aimed  at  clear- 
ness and  conciseness,  and  have  omitted  detailed  descriptions  of  in- 
vestigations and  of  apparatus  as  entirely  as  is  consistent  with  the 
foregoing  objects.  Most  of  the  experimental  illustrations  described 
or  referred  to  are  such  as  can  be  performed  in  the  lecture-room." 

The  preface  to  the  second  edition  contained  this  statement: 

"  In  the  use  of  the  book  experience  has  shown  that  many  of  the 
subjects  touched  upon  are  pregnant  with  suggestions  to  the  pupils, 
and  there  is  a  great  temptation  to  treat  them  more  fully;  but  the 
object  for  which  the  lessons  were  prepared  and  the  time  that  can 
be  devoted  to  them,  as  stated  in  the  preface  to  the  first  edition, 
are  barriers  to  a  more  extended  treatment,  or  to  a  different  ap- 
portionment of  space  to  the  subjects  treated." 

The  same  necessities,  conditions  and  objects  as  set  forth  in  the 
above  extracts  have  been  the  governing  factors  in  this  revision  for 
the  third  edition,  and  they  have  prescribed  the  same  limitations 
and  general  treatment  as  in  the  previous  editions. 

iii 


271301 


iv  PREFACE  TO   THIRD  EDITION. 

A  number  of  changes,  for  the  sake  of  simplicity  or  greater  clear- 
ness, have  been  made  both  in  the  figures  and  in  the  text  of  the 
second  edition. 

The  chapters  relating  to  meteorology  have  been,  in  large  part, 
rewritten,  and  the  author  is  entirely  indebted  to  the  published 
papers  of  Prof.  F.  H.  Bigelow,  U.  S.  Weather  Bureau,  for  new 
and  interesting  matter  in  this  science.  The  publications  of  Prof. 
Bigelow  have  shown  the  necessity  for  a  modification  of  Ferrers 
view  of  the  general  circulation  of  the  atmosphere,  and  they  con- 
tain a  new  theory  of  cyclones,  more  satisfactory  in  conception  and 
in  much  more  perfect  accord  with  observations  than  the  generally 
accepted  condensation  theory.  This  new  explanation  of  the 
cyclone  is  here  adopted  instead  of  that  given  in  the  second  edition. 

There  are  appended  to  this  edition  a  few  tables,  valuable  for 
use  or  reference. 

S.  E.  TILLMAN. 
WE  -,T  POINT,  May  15,  1901. 


PREFACE  TO  FOURTH  EDITION. 


The  conditions  which  produced  the  previous  editions  of  this 
book  and  which  have  limited  its  scope  and  governed  the  treatment 
of  the  subject  are  briefly  given  in  the  preface  to  the  third  edition 
which  preface  is  retained  herein. 

The  conditions  referred  to  are  still  such  that  no  material 
changes  in  the  book  have  been  made,  except  that  a  short  general 
description  of  steam  turbine  engines  has  been  introduced. 

S.  E.  T. 

WEST  POINT,  N.  Y,  July  i,  1907. 


CONTENTS. 


CHAPTER  I. 

THERMOMETRY. 

PAGX 

Heat  and  Temperature 1 

Effect  of  Heat— Expansion 2 

Construction  of  Thermometers 4-6 

Thermometric  Scales .  6 

Sensitiveness  of  Thermometers 8 

Advantages  of  Mercury k  8 

Alcohol  Thermometer „     .  8 

Maximum  and  Minimum  Thermometers 8 

Air  Thermometers O..ll 

Metallic  Thermometers 11 

Pyrometers 12 

CHAPTER  H. 

DILATION  OF  BODIES. 

Coefficient  of  Expansion - 13 

Expansion  of  Solids 14 

Expansion  of  Liquids 16 

Expansion  of  Gases 17 

Air  Thermometers,  Advantages  of 21 

Convection  of  Heat  in  Fluids 21 

Warming  Buildings  by  Hot  Water 21 

Draught  of  Chimneys 23 

Heating  by  Stoves 25 

Warming  by  Hot  Air 26 

Ventilation 26 

CHAPTER  IH. 

CALORIMETRY. 

Unit  of  Heat 27 

Thermal  Capacity 28 

v 


VI  CONTENTS. 

MM 

Specific  Heat 29 

Specific  Heat  of  Water 80 

Specific  Heat  of  Gases .80 

CHAPTER  IV. 

PRODUCTION  AND  CONDENSATION  OF  VAPOR. 

Vaporization     .    .    .    .    . 82 

Maximum  Density  and  Pressure  of  Vapor 82 

Influence  of  Temperature  on  Density  and  Pressure    ....          >    .     .  34 

Mixture  of  Gas  and  Vapor «         ....  88 

Condensation  of  Vapors 37 

Continuity  of  Liquid  and  Gaseous  State 87 

Liquefaction  and  Solidification  of  Permanent  Gases  .     .         37 

Conditions  affecting  Rapidity  of  Evaporation    .    .    .    .     ,     ,    .         .     .  38 

Ebullition  or  Boiling      ...         .     .............  39 

Effect  of  Pressure  on  Boiling  Point      . 41 

Other  Causes  affecting  the  Boiling  Point 42 

Applications  resulting  from  Variations  in  Boiling  Point 43 

Distillation . 44 

Spheroidal  State , 46 

CHAPTER  V. 

CHANGE  OF  STATB. 

Liquefaction— Latent  Heat  of  Fusion •....47 

Latent  Heat  of  Solution 49 

Congelation  or  Solidification  .     .     .     . 50 

Effect  of  Pressure  on  the  Freezing  and  Melting  Points 51 

Latent  Heat  of  Vaporization „ 51 

Latent  Heat  of  Expansion 53 

Utilization  of  Latent  Heat 54 

Freezing-Mixtures 54 

Cold  by  Evaporation 54 

Ice-Machines 56 

Steam-Heating 56 

CHAPTER  VL 

HYGROMETRY. 

Absolute  Humidity  < 58 

Relative  Humidity k         .    .    .  58 

Dew-Point .    .     .     „  59 

Hygroscopes e    .    .     .  59 

Hygrometers ,,....  W 


CONTENTS.  Vii 

CHAPTER  VII. 

CONDUCTION. 

PAGE 

Variable  and  Permanent  Stages 6? 

Determination  of  Conductivity    .     .     .    . .68 

Determination  of  Diffusivity 73 

Absolute  and  Relative  Conductivity 73 

Conductivity  of  Solids 74 

Conductivity  of  Liquids 75 

Conductivity  of  Gases 75 

CHAPTER  VIIL 

RADIATION. 

General  Properties  of  Radiant  Heat .....  77 

Theory  of  Exchanges .78 

Light  and  Heat  Spectra  of  Bodies 79 

Refraction  of  Heat 80 

Reflecting  Power 80 

Burning  Mirrors 81 

Irregular  Reflection  of  Heat 81 

Emissive  Power 82 

Absorption  of  Radiant  Heat 83 

Diathermancy 84 

Absorptive  and  Emissive  Power  of  Gases      .    , .  85 

Laws  of  Cooling 87 

Interference,  Polarization,  and  Refraction 88 

Distinction  between  Radiant  Heat  and  Light 89 

Selective  Absorption  and  Emission 91 

Summary  and  Conclusions 92 

CHAPTER  IX. 

THERMO-DYNAMICS. 

Heat  by  Friction 94 

Mechanical  Equivalent  of  a  Unit  of  Heat 97 

First  Law  of  Thermo-Dynamics 99 

Heat  Consumed  in  Expansion 99 

Thermic  Engines ••«.  100 

Carnot's  Cycle 101 

Principle  of  Reversibility    . • 104 

Absolute  Temperatures ........*.  105 

Steam-Engine «    .  "  108 

Double- Acting  Engine *    *    •  109 

Expansive  Working Ill 

Governors 113 

Fly-Wheels ,    .  113 


viii  CONTENTS. 

PAGH 

Compound  Engines 114 

Boilers 115 

Feeding  Apparatus 117 

Condensers 118 

Classes  of  Engines 119 

Turbine  Engines 120 

Turbine  of  De  Laval       .... 121 

Turbine  of  Curtis 123 

Turbine  of  Parsons 128 

CHAPTER  X. 

TERRESTRIAL   TEMPERATURE.       AERIAL   METEORS. 

Temperature  of  a  Place 130 

Effect  of  Altitude  upon  Temperature >     •  130 

Aerial  Meteors      .     .     t 131 

General  Circulation  of  the  Atmosphere 132 

Ferrel's  View  of  the  General  Circulation 133 

Systems  of  Winds 137 

Local  Winds 139 

Stable  and  Unstable  Condition  of  the  Atmosphere 140 

Whirlwinds 141 

Storms  .      . 142 

Cyclones 143 

Progressive  Motion  of  Cyclones 148 

Paths  of  Cyclones 149 

Low- Area  Storms 150 

Effects  of  Cyclone  and  Anticyclone  on.  Normal  Temperature 151 

Tornadoes 152 

Water-Spouts 153 

Cloud-Bursts ^54 

CHAPTER  XL 

AQUEOUS   METEORS. 

Mists,  Fogs,  and  Clouds 155 

Cloud  Formation 158 

Rain 158 

Measurement  of  Rainfall 160 

Rainfall  of  the  United  States 160 

Drv  Regions  of  the  Globe ]  60 

Snow,  Sleet,  and  Hail 161 

Dew* , 162 

Frost 163 

APPENDIX. 

I.  Problems 165 

II.  Tables  .     .  .  170 


ELEMENTARY  LESSONS  IN  HEAT. 


CHAPTER  I. 
THERMOMETRY. 

WE  are  all  familiar  with  the  sensation  of  warmth,  and  the  worda 
hot  and  cold  are  associated  in  our  minds  with  different  degrees  of 
warmth.  Heat  is  the  agent  which  produces  these  sensations,  and 
should  not  be  confused  with  the  sensations  themselves.  Heat  is  a 
form  of  energy,  and  probably  consists  in  the  energy  of  motion  of 
the  molecules  of  bodies.  This  motion  is  not  of  visible  parts  of 
matter,  but  of  the  molecules, — of  parts  too  small  to  be  observed 
separately. 

Heat  produces  in  a  body  a  series  of  different  states  or  conditions 
recognized  by  our  sense  of  heat,  and  associated  in  our  minds  with 
different  degrees  of  warmth,  indicated  by  the  terms  hot,  warm, 
cooly  cold,  etc.  In  science,  any  one  of  the  states  of  a  body  with 
respect  to  sensible  heat  is  called  its  temperature,  and  the  words  hot, 
cold,  etc.,  in  popular  use,  are  the  names  of  temperatures.  Since 
the  state  of  a  body  may  vary  continuously  from  very  hot  to  very 
cold,  there  is  an  indefinite  number  of  intermediate  states  or  tem- 
peratures. We  may  give  names  to  any  number  of  particular  tem- 
peratures and  indicate  any  other  by  its  relative  place  among  these. 
By  the  temperature  of  a  body,  therefore,  is  specified  relatively  how 
hot  it  is. 

Heat  and  Temperature. — It  is  very  essential  in  beginning  this 
subject  to  have  distinct  ideas  of  Heat,  the  agent,  and  Temperature, 
the  effect.  Without  at  present  considering  the  ultimate  nature  of 
heat,  we  may  say  that  we  know  it  to  be  a  property  of  matter,  a 
form  of  energy,  communicable  from  one  body  to  another,  so  as  to 


v    /v-kiif 

ti!tf&£%M$NTAItY  LKSSONS  IN  HEAT. 

diminish  the  quantity  of  heat  in  one  and  increase  that  in  the  other, 
and,  in  addition  to  the  changes  of  condition  in  bodies  which  heat 
produces,  and  which  we  call  temperatures,  it  produces  other  obvious 
changes,  as  changes  of  dimensions,  and  in  gases  changes  of  pressure, 
and  changes  of  state  of  aggregation,  as  in  melting  solids  or  volatiliz- 
ing liquids. 

Temperature  has  reference  to  the  states  or  conditions  of  a  body 
as  regards  sensible  heat,  these  states  usually,  but  not  always,  vary- 
ing when  heat  is  added  to  or  taken  from  a  body.  Two  unequal 
Weights  of  the  same  body  may  be  at  the  same  temperature,  but 
contain  very  unequal  quantities  of  heat,  as  may  also  two  equal 
weights  of  different  bodies  ;  thus,  a  pint  and  a  gallon  of  water  at 
the  same  temperature  will  contain  very  different  amounts  of  heat, 
as  will  also  a  pound  of  iron  and  a  pound  of  mercury.  The  temper- 
ature of  a  body  always  determines  whether,  as  regards  other  bodies, 
heat  will  flow  from  or  to  it ;  thus,  from  a  small  piece  of  metal  at 
high  temperature,  heat  will  pass  to  any  amount  of  metal,  however 
large,  at  a  lower  temperature,  though  the  larger  mass  might  con- 
tain a  much  greater  quantity  of  heat.  Temperature  is  one  of  the 
effects  of  heat ;  it  is  the  state  of  a  body  with  respect  to  its  power 
of  communicating  heat  to  other  bodies. 

It  would  probably  be  more  correct  to  say  that  temperature  de- 
termines whether  more  heat  flows  from  a  body  than  to  it,  as  all 
bodies  are  probably  giving  out  and  receiving  heat,  but  in  unequal 
quantities,  depending  upon  their  own  temperatures  and  that  of 
surrounding  bodies.  This  unequal  transfer  of  heat  always  takes 
place  whenever  bodies  at  unequal  temperatures  are  in  communica- 
tion with  each  other,  and  continues  until  an  equilibrium  of  tem- 
perature is  established.  If  no  excess  of  heat  over  that  received 
passes  from  one  body  to  another,  there  will  be  no  change  in  either, 
as  regards  heat,  and  such  bodies  are  said  to  be  at  the  same  temper- 
ature. 

Expansion. — Although  our  sensations  give  us  indications  of 
varying  temperature,  they  are  not  sufficient  for  the  accurate  com- 
parison of  the  states  of  bodies,  all  of  our  sensations  being  modified 
by  subjective  causes.  This  is  readily  perceived  by  placing  one  hand 
in  cold  and  the  other  in  hot  water  for  a  little  time,  then  by  dipping 
both  hands  in  lukewarm  water  it  will  appear  warm  to  one  hand 


THERMOMETRT. 


3 


and  cold  to  the  other.  Accompanying  variations  of  temperature  in 
bodies  there  are  usually  other  variations  in  the  properties  of  bodies, 
some  of  which  are  abrupt,  as  the  melting  of  ice  and  the  boiling  of 
water  ;  other  variations  are  continuous,  the  most  general  of  which 
is  the  expansion  or  change  of  volume  which  bodies  undergo  with 
change  of  temperature.  The  volume  of  most  substances,  under 
specified  conditions,  increases  continuously  as  the  temperature 
rises,  and  decreases  as  the  temperature  falls,  though  there  are  ex- 


FIG.  1.— GRAVESAND'S  RING. 


FIG.  3.— EXPANSION  OF  GASES. 


FIG.  2.— EXPANSION  OF  LIQUIDS. 


ceptions  to  the  rule.  This  effect  of  heat  on  bodies,  accompanying 
change  of  temperature,  may  be  illustrated  by  the  following  experi- 
ments. 

Solids. — Take  a  ring  through  which  a  metal  sphere  when  cold 
just  passes,  as  in  Fig.  1.  Heat  the  sphere,  and  it  will  no  longer 
pass  through  the  ring  :  during  a  rise  of  temperature  its  volume  has 
increased.  Let  the  sphere  be  cooled  by  immersion  in  water :  it 


4  ELEMENTARY  LESSONS  IN  HEAT. 

will  again  pass  through  the  ring,  its  volume  decreasing  with  fall  of 
temperature. 

Liquids. — Let  a  quantity  of  liquid  contained  in  a  glass  bulb 
with  a  narrow  neck  be  heated  (Fig.  2)  :  the  liquid  will  rise  in  the 
neck,  showing  an  increase  of  volume.  The  liquid  descends  slightly 
at  the  beginning  of  the  operation,  owing  to  the  fact  that  the  bulb 
is  warmed  and  increases  in  volume  before  the  liquid  expands  sensi- 
bly. When  the  liquid  is  warmed  it  expands  also,  and  as  it  rises  in 
the  neck  we  'conclude  that  it  expands  more  than  the  glass. 

Gases. — Any  gas  confined  in  a  vessel,  as  in  Fig.  3,  may,  by  the 
application  of  very  little  heat,  as  when  the  hand  is  applied  to  one 
of  the  bulbs,  be  made  to  occupy  a  sensibly  larger  volume. 

Thermometer. — This  most  general  effect  of  heat  on  bodies — the 
changes  of  volume  accompanying  changes  of  temperature — fur- 
nishes us  with  a  means  of  estimating  temperatures  which  depends 
upon  the  properties  of  matter  and  is  independent  of  our  own 
senses.  This  means  consists  in  measuring  the  change  of  volume  in 
a  body  produced  by  heat  and  accepting  this  change  to  be  the  same 
as  the  change  of  temperature.  Any  arrangement  for  measuring  or 
comparing  temperatures  may  be  called  a  thermometer.  When  such 
an  arrangement  is  at  the  same  temperature  as  the  surrounding 
medium,  it  of  course  indicates  both  its  own  temperature  and  that 
of  the  surrounding  medium.  Under  such  conditions,  therefore, 
thermometers  measure  or  indicate  the  temperatures  of  the  surround- 
ing medium. 

The  most  common  form  of  thermometer  is  the  mercurial.  It 
consists  of  a  capillary  glass  tube  terminating  in  a  bulb  or  reservoir. 
The  bulb  and  a  portion  of  the  tube  are  filled  with  mercury.  As 
the  temperature  varies  the  level  of  the  mercury  in  the  tube  will  rise 
or  fall.  These  variations  in  the  volume  of  the  mercury  measure 
the  temperature. 

The  principle  of  the  construction  of  a  mercurial  thermometer  is 
simple,  but  the  construction  of  an  accurate  thermometer  is  a  very 
delicate  operation. 

The  Tube. — It  is  evident  that  the  tube  should  be  of  as  uniform 
bore  as  possible.  This  may  be  tested  by  introducing  a  short  col- 
umn of  mercury  into  the  tube  and  moving  it  successively  forward 
through  its  length.  If  these  lengths  are  unequal,  the  tube  is  not 


THERMOMETR  Y. 


of  uniform  bore.  If  these  different  lengths  be  marked  on  the  tube 
they  will  indicate  equal  volumes,  and  the  tube  is  thus  calibrated. 

Introduction  of  Mercury. — When  a  suitable  tube  is  obtained,  one 
end  is  closed  and  expanded  into  a  bulb,  usually  by  blowing,  and  the 
other  end  is  drawn  out  somewhat  expanded  and  left  open.  The 
bulb  is  then  cautiously  heated,  and  the  open  end  inserted  into  a  cup 
of  mercury  (Fig.  5);  the  mercury  rises  in  the  tube  as  the  latter 
cools,  replacing  the  air  which  was  expanded  and  driven  out  by  the 
heat.  By  alternately  heating  and  cooling  the  bulb,  with  the  instru- 
ment upright  (Fig.  4),  a  considerable  portion  of  the  mercury  de- 
scends to  the  bulb.  By  now  boiling  the  mercury  in  the  bulb  the 
vapor  of  mercury  drives 
out  the  air  and  completely 
fills  the  tube,  and  while  in 
this  condition  the  open  end 
of  the  tube  is  plunged  into 
the  vessel  of  mercury.  As 
the  tube  cools  and  the 
vapor  of  mercury  con- 
denses, the  atmospheric 
pressure  causes  the  liquid 
mercury  to  completely  fill 
the  tube  and  bulb.  The 
thermometer  thus  filled  is 
then  heated  until  so  much  FIG.  4. 
mercury  is  driven  out  by 

expansion  that  the  remainder  in  the  tube  stands  at  the  point  re- 
quired at  common  temperatures.  This  being  adjusted,  the  heat  is 
again  applied  until  the  mercury  fills  the  tube,  and  while  thus  filled 
the  tube  is  sealed  by  fusion  with  a  blow-pipe.  The  retraction  of 
the  mercury  in  cooling  leaves  a  vacuum,  which  is  essential  to  the 
perfection  of  the  instrument. 

Reference  Points. — We  now  have  an  instrument  which  would 
indicate  temperatures,  but  to  make  its  indications  comparable  with 
similar  instruments  we  must  adopt  for  all  at  least  two  common 
points  of  reference.  For  these  points  of  reference,  or  standard 
temperatures,  it  has  been  agreed  to  adopt  the  freezing  and  boiling 
points  of  water,  or,  more  correctly,  the  tempeiature  of  a  mixture  of 
ice  and  water  under  ordinary  pressure,  and  the-  U^perature  of  steam 


FIG.  5.— INTRODUCTION  OP  MERCURY. 


6 


ELEMENTARY  LESSONS  IN  HEAT. 


from  water  boiling  under  definite  pressure.  These  two  phenomena 
are  found  always  to  give  the  same  temperatures,  they  are  easily  re- 
produced and  maintained,  and  are  consequently  our  most  important 
temperature  references. 

These  two  points  are  found  by  noting  the  level  of  the  mercury 
in  the  tube  when  subjected  to  the  conditions  indicated  in  Figs.  6 
and  7.  In  the  first  case  the  instrument  is  surrounded  by 
melting  ice  contained  in  a  perforated  vessel  to  allow  the  escape 
yf  the  water  produced;  in  the  second  case  it  is  surrounded  by 
steam  from  boiling  water,  a  small  manometer  tube  being  used  to 
show  that  the  pressure  of  the  steam  is  the  same  as  that  of  the  air, 
or  that  the  steam  is  not  gen- 
erated faster  than  it  escapes. 

These  two  points  being 
marked  on  the  tube,  it  only 
remains  to  divide  the  interval 


FIG.  6.— FREEZING-POINT 
APPARATUS. 


Fio.  7.— TEMPERATURE  OF  BOILING  WATER. 


between  them  into  equal  parts,  to  indicate  degrees.  The  number 
of  these  divisions  is  arbitrary,  and  they  are  continued  both  above 
and  below  the  fixed  points. 

Thermometrie  Scales. — The  most  common  scales  are — 
1.    Tlie  Centigrade.— lu  which  the  distance  between  the  fixed 
points  is  divided  into  100  equal  parts,  the  melting  point  of  ice  being 


THERMOMETRT. 


C,     F. 


210 


at  the  zero  of  the  scale,  and  the  boiling  point  of  water  at  100.    This 
scale  is  sometimes  called  the  Celsius  scale. 

2.  The  Fahrenheit. — In  which  the  interval  between  the  freezing 
and  boiling  points  is  divided  into  180  equal  parts,  the  melting  point 
being  at  32  and  the  boiling  point  at  212,  so  that  on  this  scale  the 
zero  point  is  32  degrees  below  the  melting  point. 

3.  The  Reaumur. — This  scale  has  80  divisions 
between  the  fixed   points,  the  zero  being  taken 
at  the  melting  point  and  80  marking  the  boiling 
point. 

The  scales  with  their  reference  points  are  in- 
dicated in  Fig.  8.  On  all  the  scales  the  numbers 
below  the  zero  point  are  distinguished  by  the 
negative  sign. 

A  little  consideration  enables  us  to  find 
equivalent  readings  on  the  other  scales  when 
that  of  any  one  is  given.  It  is  evident  that 
equal  intervals  of  temperature  on  the  scales  are 
to  each  other  as  the  numbers  180,  100,  and  80, 
or  9,  5,  and  4.  Since  the  zero  on  the  Fahren- 
heit scale  is  32°  below  the  freezing  point,  this 
number  must  be  subtracted  from  the  Fahrenheit 
reading  to  get  the  interval  from  the  freezing 
point ;  f  or  f  of  this  interval  will  then  be  the 
corresponding  reading  on  the  Centigrade  and 
Reaumur  scales,  respectively;  -f-  and  f  of  the 
Centigrade  and  Reaumur  readings,  respectively, 
will  give  the  corresponding  interval  from  the 
freezing  point  on  the  Fahrenheit  scale,  to  which 
must  be  added  32,  to  give  the  corresponding 
Fahrenheit  reading.  To  convert  the  readings 
of  the  Centigrade  and  Reaumur  scales  no  ex- 
planation is  necessary. 

The  rules  for  the  conversion  of  the  scales  are  expressed  in  the 
following  equations,  in  which  C,  F,  and  R  denote  equivalent  read- 
ings : 

C  =  JR=f(F-32), 
F  =  |C  +  32  =  |R  +  32, 
R  =  f  C  =  *(F  -  32). 


K..  C.    F. 


FIG.  8. — THERMOME- 
TER SCALES. 


8 


ELEMENTARY  LESSONS  IN  HEAT. 


Sensitiveness  of  Thermometers. — The  power  of  the  instrument 
to  detect  slight  differences  of  temperature  will  evidently  be  measured 
by  the  length  of  the  degrees,  which  will  vary  with  the  expansibility 
of  the  substance  used  arid  the  capacity  of  the  bulb  directly  and  the 
area  of  the  cross-section  of  the  tube  inversely. 

The  quickness  of  action  depends  upon  the  rapidity  with  which 
the  substance  employed  in  the  thermometer  comes  to  an  equilibrium 
of  temperature  with  the  surrounding  medium  ;  and  this  depends 
upon  the  nature  of  the  substance  (its  conducting  power  and  specific 
heat),  and  requires  that  the  bulb  be  small  in  at  least 
one  dimension  and  the  glass  of  the  bulb  thin. 

Advantages  of  Mercury. — Mercury  is  usually 
chosen  for  a  thermometric  substance,  because  of  its 
uniformity  of  expansion  within  certain  limits,  and 
because  of  the  great  interval  between  its  freezing 
point  (—  39°  C.)  and  its  boiling  point  (357°  C.). 
It  is  opaque  and  easily  seen  in  the  tube,  it  fulfils 
the  conditions  of  good  conduction  and  small  specific 
heat,  ic  does  not  wet  or  adhere  to  the  glass,  and  it 
can  be  easily  obtained  pure. 

Alcohol  Thermometer. — Other  liquids  may  be 
used  in  thermometers,  and,  for  temperatures  near 
to  and  below  the  freezing  point  of  mercury,  alcohol 
is  often  employed  because  of  its  very  low  freezing 
point  (—  130°  0.).  The  expansion  of  alcohol  is  not 
so  uniform  as  that  of  mercury,  and,  if  an  alcohol 
thermometer  be  graduated  throughout  by  compari- 
son with  a  mercurial  thermometer,  its  degrees  will 
be  longer  as  we  ascend  the  scale. 

Maximum  and  Minimum  Thermometers. — 
Besides  the  temperature  at  a  particular  instant, 
it  is  often  desirable  to  know  the  highest  or  lowest 
temperature  to  which  an  instrument  has  been  ex- 
posed. Maximum  and  minimum  thermometers  are 
used  for  this  purpose,  and  they  are  "  self -registering." 

Six's  (Fig.  9)  is  a  common  form  of  such  an  instrument  in 
popular  use,  and  is  both  a  maximum  and  a  minimum  thermom- 
eter. It  consists  of  a  glass  tube  bent  twice  upon  itself, 


/\D 

Q       ^  \r^3/  fc 

I 

9 

i? 

*t 

120 

30 
20 

110 
100 
90 

o- 

80 

Ifr 
30 

* 

70 

50 

^40 

E&z 

FR£S 

40 
50 
60 

50 

20 

70 

10 

80- 
90 
100 

\ 

10 
20 

110 
120 

^ 
_B 

40 

Fio.9.-Six's 
THERMOMETER. 

as 


THERMOMETRY. 


9 


shown  in  the  figure.  Alcohol  fills  the  bulb  C  and  a  portion 
of  the  tube  to  the  left ;  another  portion  is  occupied  by  a  column 
of  mercury,  which  extends  around  the  lower  bend  and  partly 
up  the  tube  on  the  right;  the  remainder  of  the  tube  and  a 
portion  of  the  bulb  D  is  occupied  by  alcohol ;  the  other  portion 
of  D  is  occupied  by  air.  The  mercury  column  is  in  contact  with 
the  alcohol  at  both  extremities,  and,  when  by  an  elevation  of  tem- 
perature the  alcohol  in  C  expands,  it  shoves  the  mercury  column 
before  it.  The  highest  points  reached  in  the  right  and  left  limbs 
of  the  instrument  by  the  ends  of  the  mercurial  column  are  indi- 
cated by  two  indices,  held  in  place  by  springs  just  strong  enough 
to  keep  them  from  slipping  by  their  own  weight.  The  expansion  of 
the  air  in  D  causes  the  mercury  column  to  follow  the  alcohol  during 


FIG.  10. — RUTHERFORD'S  MAXIMUM  AND  MINIMUM  THERMOMETERS. 

contraction.  It  is  readily  seen  from  the  figure  that  the  maximum 
temperature  is  recorded  on  the  right  scale,  and  the  minimum  on 
the  left.  The  indices  must  in  part  be  composed  of  iron  or  steel,  so 
that  they  can  be  brought  to  the  surface  of  the  mercury  by  a  magnet. 
The  alcohol  in  the  right  limb  of  the  tube  prevents  the  index  from 
rusting. 

Rutherford's  maximum  and  minimum  thermometers  are  distinct 
instruments,  though  often  mounted  together,  as  in  Fig.  10,  both 
being  placed  horizontally.  The  liquid  of  the  minimum  is  alcohol, 
and  has  immersed  in  it  a  small  index  of  glass  or  enamel.  To  set  the 
instrument  it  is  inclined  until  the  forward  end  of  the  index  slides 
to  the  end  of  the  liquid  column.  During  the  expansion  of  the 
liquid  the  index  remains  stationary,  the  liquid  moving  by  it ;  but 
during  contraction  the  end  of  the  liquid  column  does  not  pass  the 


10 


ELEMENTARY  LESSONS  IN  HEAT. 


index  but  pulls  it  back.  The  forward  end  of  the  index  thus  marks 
the  degree  of  contraction  of  the  liquid,  and  hence  the  minimum 
temperature  reached. 

The  liquid  of  the  maximum  thermometer  is  mercury,  and  the 
tube  contains  an  iron  or  steel  index  outside  the  mercury.  This 
index  is  pushed  before  the  mercury  during  expansion  and  is  left 
behind  during  contraction.  The  back  end  of  the  index  marks  the 
limit  of  expansion,  and  therefore  the  maximum  temperature  expe- 
rienced. The  instrument  is  set  by  bringing  the  index  back  to  the 
mercury,  and  this  is  usually  done  with  a  magnet. 

Phillips' 's  Maximum  Thermometer. — In  this  instrument  the 
index  is  a  part  of  the  mercurial  column  itself,  separated  from  the 
main  body  of  the  liquid  by  a  little  air,  as  shown  in  Fig.  11. 


lo.  11.—  PHILLIPS'S  MAXIMUM  THERMOMETER. 


Another  form  of  maximum  thermometer  is  that  of  Negretti, 
shown  in  Fig.  12.     The  bore  of  the  tube  is  diminished  at  a;  dur- 


FIG.  12.— NEGRETTT'S  MAXIMUM  THERMOMETER. 

ing  expansion  the  mercury  is  forced  through  at  n.  but  during  con- 
traction the  part  of  the  column  past  the  obstruction  does  not  re- 
turn. To  set  this  instrument  the  detached  column  must  be  shaken 
past  the  contraction  until  the  bulb  is  filled  and  the  column  con- 
tinuous. 


2  'HEliMOMEl  R  T. 


11 


Air  Thermometers.— Air  or  other  gas  may  be  used  as  a  thermo- 
metric  fluid,  and  such  instruments  will  measure  temperatures 
through  a  very  wide  range.  They  may  be  constructed  either  upon 
the  principle  that  the  volume  of  the  gas,  at  constant  pressure,  varies 
directly  with  the  temperature,  or  that,  if  the  volume  be  kept  con- 
stant, the  pressure  varies  in  the  same  way.  Such  instruments  are 
the  most  accurate  of  all  thermometers,  and  will  be  again  alluded  to. 

Metallic  Thermometers. — Thermometers  depending  upon  the 
expansion  of  solids  by  heat  have  been  made.  For  domestic  purposes 
a  very  convenient  thermometer  of  this  kind  is  now  widely  used  in 
this  country.  It  is  made  by  the  "Standard  Thermometer  Com- 
pany," Peabody,  Mass.  Its  great  convenience  centres  mainly  in 
the  large  dial-face,  upon  which  the  temperature  is  indicated  by  a 
pointer.  These  faces  are  as  much 
as  eight  inches  in  diameter,  and  the 
temperature  can  be  observed  from  a 
distance  of  fifteen  feet.  In  the 
largest  and  best  forms  a  ribbon 
three- sixteenths  of  an  inch  wide, 
composed  of  two  strips  of  metal  sol- 
dered together  (apparently  brass 
and  steel),  is  closely  wound  into  a 
cylindrical  spiral  two  inches  long 
and  five-eighths  of  an  inch  in  di- 
ameter. One  end  of  this  spiral  is 
rigidly  attached  to  a  fixed  support, 
and  the  other  is  made  fast  to  the 
centre  of  a  brass  octant,  the  octant 
itself  being  mounted  on  an  axis 
passing  through  the  middle  point 
of  its  bisecting  radius.  The  rim  of 
the  octant  is  cut  into  cogs,  which 
work  into  the  teeth  of  a  smaller 
wheel.  The  axis  of  the  smaller 

Wheel  projects  in  front   of  the  dial-        F'°-  ^-METALLIC  THERMOMETER. 

face  and  carries  the  pointer.  The  winding  and  unwinding  of  the 
ribbon,  due  to  contraction  and  expansion,  by  this  gearing  transmit 
motion  to  the  pointer. 


12  ELEMENTARY  LESSONS  IN  HEAT. 

The  actuating  part  of  a  simpler  form  made  by  the  same  company 
is  shown  in  Fig.  13,  in  which  a  is  a  circular  compound  metal 
ribbon  with  one  end  attached  to  the  semicircular  brass  hoop  b. 
From  the  ends  of  this  hoop  a  small  cord  passes  to  and  several  times 
around  the  axis  d,  whose  back  end  abuts  against  the  supporting 
strip  g.  The  axis  passes  through  the  frame-plate  P  and  through 
the  dial-plate  in  front  of  it,  and  its  other  end  carries  the  pointer. 
Since  the  cord  is  so  wound  that  it  cannot  slip,  it  is  evident  that 
expansion  or  contraction  in  the  ribbon  produces  rotation  in  the  axis 
and  corresponding  motion  in  the  pointer.  Owing  to  the  care  exer- 
cised in  the  adjustment  of  these  instruments,  they  compare  favora- 
bly in  accuracy  with  ordinary  mercurial  thermometers,  and  are  far 
more  convenient.  Much  older  forms  of  metallic  thermometers, 
very  similar  in  principle  to  the  above,  have  long  been  made,  but 
have  not  come  into  general  use. 

Pyrometers. — Other  instruments  are  also  constructed  for  meas- 
uring very  high  temperatures,  as  those  of  furnaces,  and  are  called 
Pyrometers.  Wedgwood's  pyrometer  acts  by  the  measurement  of 
the  contraction  in  a  piece  of  baked  clay  when  heated.  Other  in- 
struments of  this  class  depend  for  their  action  upon  the  expansion 
of  a  metal  rod  (iron,  platinum,  etc.),  contained  in  an  infusible 
cylinder,  the  expansion  giving  motion  to  an  indicator  of  some  kind. 


CHAPTEE  II. 
DILATION    OF   BODIES. 

Coefficient  of  Expansion. — It  has  been  stated  as  a  general  though 
not  universal  law,  that,  when  the  temperature  of  a  body  is  increased 
(other  conditions  being  unchanged),  its  volume  is  also  increased, 
and  the  reverse.  The  temperature  and  volume  vary  simultaneously, 
and  the  quantity  which  expresses  the  average  numerical  relation 
between  the  variations  of  volume  for  each  unit  of  temperature,  and 
the  original  volume  taken  at  a  standard  temperature,  is  the  mean 
coefficient  of  cubical  expansion. 

Thus,  let  a  substance,  whose  volume  is  v,  at  a  standard  tempera- 
ture ty  assume  a  volume  vl  at  a  temperature  tl ;  then  the  change  of 
temperature  is  t\  —  t,  the  corresponding  change  of  volume  in  terms 

of  original  volume  is  -     — ,  and  the  quotient      *       >  =  a  is  the 

mean  coefficient  of  cubical  expansion  between  the  temperatures 
ti  and  t. 

The  coefficient  of  cubical  expansion  of  a  substance  is  made 
specific  by  defining  it  as  the  ratio  which  the  increase  in  unit  volume 
bears  to  the  unit  of  volume  when  the  temperature  of  the  unit  is 
raised  from  0°  C.  to  1°  C.  In  other  words,  if  in  the  equation 


(t,  -  t) 

we  make  v  =  1,  tv  =  1°  C.,  and  t  =  0°  C.,  a  becomes  the  specific 
coefficient  of  expansion.  If  the  body  is  homogeneous  and  it  be 
raised  to  the  same  temperature  throughout,  it  is  unnecessary  to 
consider  the  unit  of  volume. 

The  coefficient  of  cubical  expansion  of  any  substance  at  any 
temperature  is  the  ratio  which  the  increase  of  volume  bears  to  the 
original  volume  when  its  temperature  is  raised  one  degree.  The 

13 


H  ELEMENTARY  LESSONS  IN  HEAT. 

expression  for  the  mean  coefficient  of  expansion  between  tl  and  t, 


__ 

a  =  -~  --  —  ,  becomes  the  expression  for  the  coefficient  of  expan- 

sion at  temperature  t  when  £,  —  t  is  made  equal  to  unity. 

If,  instead  of  considering  the  increments  of  volume  produced  by 
heat,  we  estimate  the  increase  in  length  or  superficial  area,  the  cor- 
respondiDg  increments  become  the  coefficients  of  linear  and  super- 
ficial expansion,  respectively. 

The  coefficient  of  linear  expansion  at  any  temperature  is  the 
ratio  which  the  increment  in  length  of  the  body  bears  to  the 
original  length,  when  the  temperature  is  raised  one  degree.  As  in 
cubical  expansion,  if  no  temperature  is  specified,  reference  is  had  to 
the  increase  in  length  between  0°  and  1°  C. 

It  will  be  inferred  from  the  foregoing  definitions  that  the  varia- 
tions in  the  dimensions  of  bodies  are  not  always  exactly  propor- 
tional to  variations  of  temperature,  and  such  is  found  to  be  the 
case:  at  high  temperatures  the  coefficients  of  expansion  increase 
slowly  as  the  temperatures  rise. 

Solids.  —  Since  the  change  of  dimensions  in  solids  for  a  change 
of  one  degree  in  temperature  is  very  small,  the  mean  coefficient  of 
expansion,  the  specific  coefficient,  and  the  coefficient  at  a  particular 
temperature  for  moderate  ranges  of  temperature,  may  be  taken  for 
ordinary  considerations  to  be  the  same.  It  is  usually  the  first  that 
we  determine.  Thus,  the  ratio  which  the  increase  of  length  in  a 
bar  of  metal  between  0°  and  1°  C.  bears  to  the  original  length  at  0° 
is  taken  as  the  T-J-7  of  the  ratio  between  0°  and  100°  C.  Supposing 
J0  and  ZJOO  to  represent  the  lengths  of  the  rod  at  0°  and  at  100°,  re- 

spectively, we  have  -^-  —  -  =  100  a,  or  a  =  Tiir  —  —  —  -,  the  coeffi- 

^0  % 

cient  of  linear  expansion.  The  coefficient  of  expansion  of  solid 
metals  is  sensibly  constant  from  0°  to  100°  C.,  but  above  that  point 
it  becomes  irregular. 

Relation  between  Cubical  and  Linear  Expansion.  —  In  general, 
homogeneous  uncrystallized  bodies  expand  in  such  manner  that  the 
figures  at  different  temperatures  are  similar,  or  expand  equally  in 
all  directions.  In  such  cases  the  cubical  expansion  for  small 
changes  of  temperature  is  approximately  three  times  the  linear. 
For,  suppose  the  body  to  be  divided  into  any  number  of  cubes,  and 
let  v  represent  the  volume  of  a  cube  whose  edge  may  be  taken  as 


DILATION  OF  BODIES.  15 

unity.  After  expansion  the  length  of  an  edge  will  be  1  -f-  /,  and  the 
volume  will  become  (1  -f  /)'  or  1  +  3/  -f-  3/3  -f  I3.  If  I  is  so  small 
that  higher  powers  than  the  first  may  be  omitted  without  material 
error,  we  have  the  cubical  expansion  equal  to  3?  ;  that  is,  three 
times  the  same  fraction  of  the  volume  that  the  linear  expansion  is 
of  the  length.  If  the  body  does  not  expand  equally  in  all  directions, 
let  a,  b,  and  c  denote  the  expansion  of  the  three  conterminous  edges 
at  right  angles  to  each  other,  then  the  volume  in  expanding  will 
become  (1  -)-  a)  (1  +  b)  (1  -j-  c)  or  1  +  a  -f  b  +  c  -J-  ab  +  ac  -\-  be 
-(-  abc  ;  and  if  a,  b,  and  c  are  very  small,  as  is  usually  the  case  with 
solids,  their  products  may  be  omitted,  and  the  cubical  expansion, 
for  small  changes  of  temperature,  is  in  all  cases  approximately  equal 
to  the  sum  of  the  expansions  of  length,  breadth,  and  thickness  ex- 
pressed in  terms  of  the  volume. 

Considering  in  the  same  way  the  expansion  in  area,  it  is  readily 
seen  that  the  surface  expansion  is  twice  that  of  the  linear  in 
isotropic  bodies,  and  in  other  bodies  it  is  equal  to  the  sum  of  the 
expansions  in  length  and  breadth  expressed  in  terms  of  the 
surface. 

Force  Exerted  in  Expansion. — The  force  which  is  required  to 
change  the  volume  of  a  solid  by  a  certain  amount  is  the  same  as 
that  which  the  solid  would  exert  during  a  change  of  temperature 
sufficient  to  produce  the  same  change  in  its  volume.  It  has  been 
calculated  that  a  bar  of  wrought-iron  of  square  cross-section,  four 
inches  on  a  side,  would  exert  a  pull  of  sixteen  tons  if  its  ends  were 
secured  and  its  temperature  should  fall  15°  F.  Consequently,  in 
all  structures  where  metal  is  largely  used,  and  which  are  subjected 
to  considerable  changes  of  temperature,  it  is  indispensable  to  make 
provision  for  these  changes  of  dimension.  The  force  of  contracting 
metal  is  frequently  made  use  of  to  straighten  up  walls  which  have 
settled  and  inclined.  This  is  done  by  securing  bars  of  iron  in  a 
heated  state  to  the  walls  so  that  the  force  of  contraction  in  cooling 
is  exerted  to  pull  them  together. 

The  amount  of  linear  expansion  of  glass  in  passing  from  0°  to 
100°  C.  is  yyV^j  and  of  platinum  it  is  J^T-  The  fact  that  these 
two  substances  expand  so  nearly  equally  enables  us  to  fuse  a  plat- 
inum wire  into  a  glass  tube  without  fear  of  breakage  on  cooling. 

There  are  some  interesting  exceptions  to  the  law  that  the  vol- 
umes of  bodies  increase  with  the  temperatures,  and  the  statement 


16  ELEMENTARY  LESSONS  IN  HEAT. 

that  a  body  recovers  its  original  volume  when  it  returns  to  its  origi- 
nal temperature  is  not  absolutely  correct.  The  time  and  manner  of 
cooling  a  body  in  many  cases  influence  the  volume  assumed:  this 
t'act  will  be  brought  out  as  we  proceed. 

Liquids.  —  Since  liquids  must  be  retained  in  vessels,  and  since 
the  volumes  of  these  vessels  change  with  the  temperature,  it  is  evi- 
dent that  a  change  of  volume  in  the  liquid  is  complicated  with  the 
change  in  the  vessel.  The  actual  change  of  volume  of  the  liquid, 
independent  of  variations  in  the  containing  vessel,  is  the  real  or 
absolute  dilation  of  the  liquid  ;  the  apparent  dilation  is  affected  by 
the  dilation  of  the  vessel.  The  expansions  of  liquids  are,  in  gen- 
eral, much  greater  than  those  of  solids,  and  much  less  uniform,  in- 
creasing more  rapidly  as  the  temperature  rises. 

The  absolute  dilation,  between  0°  and  100°  C.,  of  alcohol,  watbr, 
and  mercury,  is  given  in  the  following  table  : 


Alcohol  expands 
Water  expands  ... 
Mercury  expands 


Mercury.  —  The  rate  of  expansion  of  mercury  increases  as  tho 
temperature  rises.  The  expansion  from  0°  to  20°  is  more  than 
double  that  from  0°  to  10°,  and  that  from  0°  to  100°  is  more  than 
ten  times  that  to  10°  and  more  than  twice  that  to  50°.  The  expan- 
sion of  mercury,  however,  is  less  variable  than  that  of  any  other 
substance  that  is  liquid  at  ordinary  temperatures,  and  the  increased 
expansibility  between  100°  and  200°  in  the  thermometer  is  nearly 
compensated  for  by  the  expansion  of  the  glass. 

Water.  —  Water  exhibits  a  striking  peculiarity  in  its  variations  of 
volume  during  change  of  temperature,  a  peculiarity  which  has  most 
important  influences.  If  fresh  water  be  taken  at  common  tempera- 
ture and  cooled  down,  its  volume  diminishes  until  the  temperature 
falls  to  about  4°  C.  After  this  a  further  reduction  of  temperature 
causes  expansion,  which  continues  until  the  freezing-point  is  reached, 
when  there  is  a  sudden  and  violent  enlargement.  At  the  tempera- 
ture of  4°  C.  water  is  at  its  maximum  density,  and  increase  or  re- 
duction of  temperature  has  the  same  effect  upon  its  volume. 

This  peculiarity  of  water  is  easily  illustrated  by  an  arrangement 
which  indicates  the  changes  of  volume  as  the  temperature  is 
changed.  A  moment's  consideration  will  show  that  this  property  of 


DILATION  OF  BODIES.  17 

water  has  a  most  beneficial  effect  in  nature.  In  cold  weathec 
bodies  of  fresh  water  are  cooled  at  the  surface,  contraction  of  vol- 
ume with  increased  density  takes  place,  the  heavier  surface  water 
descends  and  the  warmer  rises  to  replace  it.  This  circulation  con- 
tinues until  the  entire  body  of  water  falls  to  4°,  after  which  any 
further  cooling  expands  the  water  and  the  colder  water  remains  at 
the  surface.  The  freezing  of  the  surface  water  then  further 
protects  the  remaining  mass  of  water  from  other  reduction  of  tem- 
perature. 

The  gradual  expansion  of  water  between  4°  and  0°  must  be  dis- 
tinguished from  the  sudden  enlargement  in  freezing.  Many  other 
bodies,  in  common  with  wjter,  possess  this  latter  property.  The 
sudden  expansion  of  water  due  to  freezing  exerts  an  enormous 
pressure.  The  bursting  of  water-pipes  by  freezing  too  often  illus- 
trates this  force.  The  freezing  of  the  water  absorbed  by  and  taken 
into  the  crevices  of  rocks  is  a  potent  agent  of  their  disintegration. 
The  beautiful  columnar  effect  produced  by  the  freezing  of  certain 
damp  soils  is  familiar  to  all,  and  is  often  very  destructive  to  newly- 
sprouted  cereals.  Iron  shells  filled  with  water  may  be  burst  by 
subjecting  them  to  cold  enough  to  freeze  the  water. 

Sea-water  has  no  point  of  maximum  density  above  its  freezing 
point,  but  contracts  as  it  cools  until  it  solidifies  at  —  2.6°  C. 

Gases. — In  gases  the  coefficient  of  expansion  is  much  larger 
than  in  solids  or  liquids,  and  much  more  nearly  uniform  at  differ- 
ent temperatures.  Let  us  take  v0  to  indicate  the  volume  of  a  gas 
at  0°  0.,  and  vt  the  volume  at  any  other  temperature  t°;  then,  if 
the  pressure  be  the  same  at  the  two  temperatures,  the  variation  of 
rolume  is  expressed  by  the  equation 

vt  =  v0(l  +  at\ 

which  experimental  law  is  called  the  law  of  Charles  or  Gay-Lussac, 
in  which  a  is  the  mean  coefficient  of  expansion  between  0°  and  t°. 
a  has  been  shown  to  be  practically  the  same  for  all  temperatures 
within  the  range  of  the  mercurial  thermometer;  it  is  not  only  the 
same  at  different  temperatures,  but  is  the  same  for  different  gases. 
Its  value  is  approximately  .00366  or  ^^-  of  the  volume  at  0°  0.  for 
each  degree  centigrade,  nor  is  it  affected  by  the  elastic  force  or 


18  ELEMENTARY  LESSONS  IN  HEAT. 

pressure  of  the  gas.  Although  a  is  thus  practically  constant  for  all 
gases,  under  all  pressures,  and  at  all  temperatures,  it  is  not  abso- 
lutely so  :  there  are  very  slight  variations  in  different  gases  and  in 
the  same  gas  at  different  pressures,  the  greatest  deviations  being  in 
case  of  gases  most  easily  condensed. 

From  this  experimental  law  of  Charles,  which  may  be  written 

Vt  =  V°  +  273*'° ' 

it  is  seen  that  a  gas  expands  or  contracts  -^-g-  of  its  volume  at  0°  C. 
for  each  change  of  one  degree  in  temperature  on  that  scale;  there- 
fore if  its  temperature  were  reduced  to  —  273°  C.,  and  the  law  of 
volumetric  change  did  not  vary,  the  volume  of  the  gas  would  be 
reduced  to  zero.  This  temperature,  273°  below  0°  C.,  is  called  the 
absolute  zero  of  temperature,  and  temperatures  reckoned  from  this 
point  are  called  absolute  temperatures.  Since  the  absolute  zero 
is  273°  below  the  zero  ordinarily  used,  it  is  evident  that  absolute 
temperatures  in  C.  degrees  can  be  obtained  from  common  centi- 
grade readings  by  adding  273  thereto.  By  transferring  to  the  F. 
scale  it  will  be  seen  that  the  coefficient  of  expansion  on  this  scale 
is  T|~g-  (exactly  j-gV.r)  °f  the  volume  at  0°  F.  It  thus  appears  that 
the  absolute  zero  on  this  scale  is  460°  below  0°  F.,  and,  accord- 
ingly, absolute  temperatures  in  F.  degrees  may  be  obtained  by 
adding  460  to  the  common  F.  readings. 

From  the  expression  for  the  law  of  Charles, 

vt  =  v,(l  +  at), 

we  can  readily  find  what  a  volume  of  a  gas  at  one  temperature 
becomes  when  its  temperature  is  changed. 

If  the  volume  of  a  gas  is  given  at  0°  C.,  the  volume  at  any  other 
temperature  may  be  directly  obtained  by  substituting  in  the  for- 
mula the  values  of  v0 ,  t,  and  a  ;  if  t  is  below  zero,  it  has  the  nega- 
tive sign.  Thus,  required  to  know  what  200  cubic  inches  of  a  gas 
at  0°  C.  will  become  at  20°  C. 

i 
v0  =  200;     t  =  20;     a  = 

Hence  the  volume  required, 

4-  —  \ 


DILATION  OF  BODIES.  19 

If  the  volume  of  a  gas  is  given  at  a  temperature  other  than  0°  C.f 
as  for  instance  at  t,  and  then  the  volume  at  another  temperature, 
as  tl ,  is  desired,  we  have,  first, 


t 
v.  i  vt  ::  1 : 1  +  w** 


v9:vtl ::  1:1  +       ; 


and  also 


hence, 

vt:  vtl  ::  273  -f  t :  273  +  *a. 

If  the  temperatures  are  given  on  the  Fahrenheit  scale,  the  co- 
efficient of  expansion  is  ^j^ ,  the  volume  at  0°  F.  being  the  stand- 
ard, and  the  change  of  volume  will  be  determined  by  the  following 
relation  : 

vt  :  vtl  : :  460  +  t  :  460  +  t,. 

From  these  considerations  we  see  that,  with  pressure  constant, 
the  volume  of  a  gas  varies  as  its  absolute  temperature.  The  co- 
efficient of  expansion  being  constant,  it  follows  that  it  is  at  any 
temperature  numerically  equal  to  unity  divided  by  this  tempera- 
ture expressed  on  the  absolute  scale. 

Another  experimental  law  is  that  of  Boyle,  sometimes  desig- 
nated as  Mariotte's  law,  which  asserts  that  the  volume  of  a  gas  is 
inversely  proportional  to  the  pressure  when  the  temperature  re- 
mains constant,  or,  under  these  conditions,  the  product  of  pressure 
and  volume  is  constant  and  it  may  be  written  pv  =  constant. 

From  a  combination  of  Charles'  and  Boyles'  laws  two  important 
deductions  may  be  made. 

Let  P0  and  F0  be  corresponding  pressure  and  volume  of  a  mass 
of  gas  at  0°  C.  Suppose  the  pressure  be  kept  constant  and  that  the 
temperature  of  the  gas  be  changed  to  t°,  then,  by  Charles'  law,  the 
new  volume  will  be  F0  (1  +  at) ;  since  the  pressure  has  not  changed 
it  is  still  P0. 

Keep  t  constant  and  change  the  pressure  to  Pt ;  the  correspond- 
ing volume  may  be  represented  by  Vt.  Corresponding  sets  of  vol- 
umes and  pressures  at  t°  are  then  PQ  and  F0  (1  +  at)  and  Pt  and 
Vr  Applying  Boyle's  law  to  these  we  have 


20  ELEMENTARY  LESSONS  IN  HEAT. 

which  being  of  exactly  the  same  form  as  the  original  equation  for 
Charles'  law  shows  that  the  product  of  the  pressure  and  volume  of 
a  gas  will  vary  as  the  absolute  temperature. 

Make  Vt  =  F0,  which  imposes  the  condition  of  varying  the  pres- 
sure of  the  gas  with  the  temperature  without  changing  the  volume, 
and  the  equation  reduces  to 

Pt  -  P0  (1  +  at), 

which  shows  that  volume  constant  the  pressure  of  a  gas  will  vary 
as  the  absolute  temperature. 

If  we  assume  the  formula  PtVt  =  P0 F0  (1  -f-  at)  to  hold  for  all 
temperatures,  it  is  evident  that  the  first  member  becomes  0  when. 
in  the  second  member  t  =  —  273 ;  that  is,  under  the  assumption, 
that  the  laws  of  Charles  and  Boyle  are  accurate  at  all  temperatures 
the  pressure  or  volume  disappears  at  —  273°  C.  This  is  the  point 
at  which  a  gas  would  cease  to  have  volume  or  cease  to  exert  pres- 
sure on  the  walls  of  the  enclosing  vessel,  and  would  be  the  absolute 
zero  of  temperature.  This  location  of  the  absolute  zero  is  substan- 
tiated by  determinations  independent  of  the  properties  of  particular 
substances. 

Air  Thermometers. — From  what  was  said  in  regard  to  measur- 
ing temperatures  by  ordinary  thermometers,  it  is  evident  that  we 
really  measure  the  apparent  expansion  of  some  liquid  in  a  tube. 
It  is  obvious  that  we  may  make  the  indications  of  any  number  of 
these  thermometers,  containing  different  liquids,  agree  at  two  fixed 
temperatures;  but  if  the  intervals  between  these  fixed  points  on  the 
different  instruments  be  divided  into  the  same  number  of  equal 
parts,  and  all  the  instruments  be  plunged  into  a  bath  at  inter- 
mediate temperature,  no  two,  in  general,  will  indicate  precisely  the 
same  temperature,  nor  would  they  at  temperatures  beyond  the  fixed 
points,  for  different  liquids  expand  not  only  by  different  amounts, 
but  by  amounts  which  are  not  proportional.  If  all  the  instruments 
contain  the  same  liquid,  and  have  been  carefully  made,  their  indica- 
tions for  temperatures  between  and  beyond  the  fixed  points  will  be 
identical,  but  as  yet  we  have  no  reason  for  assuming  that  one  liquid 
gives  more  correctly  the  temperature  than  any  other. 


DILATION  OF  BODIES.  21 

In  case  of  permanent  gases,*  expanding  under  constant  press- 
ure, this  discordance  is  much  less,  so  that,  if  we  have  a  series  of 
thermometers  containing  permanent  gases,  and  their  envelopes  are 
of  the  same  material,  and  they  all  have  a  common  volume  under  a 
common  pressure  at  0°,  they  will  also  have  a  common  volume  under 
a  common  pressure  at  100°,  or  at  any  other  temperature.  This  fact 
would  indicate  that  for  measuring  temperatures  by  differences  of 
volume  gases  are  superior  to  liquid?.  Moreover,  the  expansion 
of  gases  is  much  greater  than  that  of  liquids,  so  that  the  expan- 
sion of  the  containing  vessel  is  much  less  important  than  with 
liquids. 

Convection  of  Heat  in  Fluids. — From  the  action  of  heat  '.n 
dilating  bodies  it  is  evident  that,  if  the  different  parts  of  a  liquid 
or  gas  are  unequally  heated,  the  warmer  portions  will  be  more 
expanded  and  become  less  dense,  while  the  cooler  portions, 
being  more  dense,  will  descend,  thus  establishing  convection 
currents. 

The  warming  of  water  is  thus  readily  brought  about  if  the 
vessel  containing  it  be  heated  at  the  bottom,  for  the  convection 
currents  just  described  are  produced,  and  a  circulation  established 
which  may  be  rendered  visible  by  coloring  matter,  cotton-seed,  or 
other  floating  particles  placed  in  the  water.  The  mass  of  water  is 
thus  heated  by  the  different  parts  alternating  in  position  and 
coming  successively  near  the  source  of  heat,  and  by  the  com- 
mingling of  the  warm  with  the  cold  water. 

Warming  Buildings  by  Hot  Water. — This  is  a  useful  domestic 
application  of  the  principle  above  stated.  A  common  and  simple 
arrangement  for  warming  buildings  is  shown  in  Fig.  14.  It  con- 
sists of  a  boiler  heated  by  a  furnace  fire.  From  the  top  of  the 

*  By  permanent  gases  are  here  meant  those  which  are  remote  from  their 
condensing  points,  and  most  nearly  in  the  condition  of  a  "  perfect  gas,"  or  one 
which  will  exactly  fulfill  Boyle's  law.  Molecular  theories  lead  to  the  conclusion 
that  for  perfect  gases  the  coefficients  of  expansion  would  be  equal.  Actual  ex- 
periment shows  that  the  more  highly  rarefied  the  gases  are,  the  more  nearly  they 
approach  to  perfect  gases  ;  and  the  more  they  are  compressed,  and  the  more 
nearly  they  approach  their  condensing  points,  the  more  they  depart  from  the 
condition  of  "  perfect  gases." 


22 


ELEMENTARY  LESSONS  IN  HEAT. 


boiler  a  pipe,  as  shown,  lead?  to  a  reservoir  in  the  upper  story  of 
the   house,  a  second  pipe  leads  from  this  reservoir  into  another 


FIG.  14.— WARMING  BY  HOT  WATER. 


reservoir  in  the  story  below,  and  thence  to  a  third,  ar-d  fiully 
enters  the  boiler  at  the  bottom. 


DILATION  OF  BODIES.  23 

The  boiler,  pipes,  and  reservoirs  are  all  filled  with  water  except 
a  small  space  at  the  top  of  the  upper  reservoir,  which  is  left  to  give 
room  for  the  expansion  of  the  liquid.  When  the  liquid  is  heated  it 
is  evident  that  a  current  will  flow  upward  by  the  pipe  from  the  top 
of  the  boiler  and  return  by  the  one  at  the  bottom.  The  great 
specific  heat  of  water,  a  property  which  we  shall  define  subse- 
quently, renders  heating  by  this  method  very  regular. 

On  American  railways  the  passenger  coaches  are  frequently 
heated  on  this  same  principle,  a  strong  solution  of  salt  being  used 
instead  of  pure  water,  which  avoids  the  liability  to  freezing  at  the 
temperature  at  which  it  would  ordinarily  occur. 

Draught  of  Chimneys. — The  expansion  of  air  by  heat  pro- 
duces the  draught,  which  for  equal  cross-section  will  depend 
mainly  upon  the  height  of  the  chimney  and  the  difference 
between  the  temperature  inside  and  outside.  It  is  because  of 
this  latter  condition  that  the  draught  is  not  so  good  when  the  fire 
is  first  lighted ;  it  also  explains  why,  if  the  temperature  of  the  room 
is  kept  constant,  the  draught  is  better  in  cold  weather  than  in 
warm.  The  location  of  the  chimney  in  the  building  would  have 
an  important  influence  in  this  respect,  as  would  also  the  form  and 
area  of  the  cross-section  of  the  chimney. 

In  ordinary  chimneys  and  fireplaces  it  is  desirable  that  the 
air  which  enters  the  chimney  should  pass  as  much  as  possible 
through  the  burning  fuel,  thus  serving  the  purposes  of  combustion 
and  being  itself  raised  in  temperature.  The  fireplace  should  not, 
then,  be  too  wide  nor  the  opening  above  the  fire  too  high.  The 
blower  facilitates  combustion  in  grate-fires  by  accomplishing  the 
above  desiderata. 

The  custom,  first  suggested  by  Kumford,  of  placing  inclined 
plates  at  the  sides  and  top  of  the  fireplace  is  a  good  one,  both  to 
guide  the  air  to  the  fire  and  to  reflect  and  radiate  the  heat  into  the 
room. 

In  an  ordinary  fireplace  (Fig.  15)  about  seven-eighths  of  the 
heat  from  the  burning  fuel  passes  up  the  chimney,  so  that  it  is  not 
an  economical  means  of  heating,  but,  on  the  other  hand,  it  is  the 
most  healthy,  as  it  produces  a  constant  change  of  atmosphere  in  the 
room,  thus  insuring  ventilation,  which  is  not  at  all  accomplished 
in  heating  by  hot  water. 


24 


ELEMENTARY  LESSONS  IN  HEAT. 


The  waste  of  heat  is  greatly  reduced  when  the  chimney  is  cen- 
trally situated,  in  which  case  as   the  heated  gases  escape  up  the 


FIG.  15. — COMMON  FIREPLACE. 


FIG.  16.— VENTILATING  FIREPLACE. 


shaft   they  warm   the   contiguous   rooms   through    which    it   suc- 
cessively passes. 

This  waste  is  still  further  prevented  in  the  so-called  ventilating 
fireplaces  (Fig.  16),  now  frequently  made,  especially  on  the  conti- 
nent of  Europe.  In  these  fireplaces  the  flue  of  the  chimney  is  not 
formed  by  a  single  passage-way  left  in  the  wall.  The  flue  and  irs 
walls  form  a  sort  of  pipe  (the  flue  frequently  is  a  cast-iron  pipe) 
which  passes  up  within  the  walls  of  the  building,  but  separated 
from  them  by  an  open  space.  In  this  open  space  around  the  flue- 
shaft  air  from  the  exterior  circulates  and  is  warmed  by  the  heat  of 


DIL A  TION  OF  BODIES.  25 

the  flue-shaft ;  at  suitable  points  above,  this  warm  air  is  admitted 
into  the  rooms  of  the  building. 

Heating  by  Stoves. — Stoves  constitute  a  far  more  economical 
means  of  heating  than  fireplaces;  from  eight-tenths  to  nine-tenths 
of  the  heat  produced  by  the  fuel  can  be  given  out  to  the  rooms  by 
closed  stoves,  such  as  are  frequently  used.  The  amount  of  air  which 
passes  per  hour  through  these  stoves  for  the  combustion  of  anthra- 
cite coal  is  not  over  one-tenth  the  volume  of  m  the  space  warmed,  so 
that  the  entire  air  of  this  space  would  only  change  once  in  ten 
hours.  A  common  chimney  and  fireplace  properly  constructed  re- 
move in  one  hour  five  times  the  whole  contents  of  the  room  it  is 
intended  to  warm. 

In  addition  to  these  disadvantages  stoves  cause  great  differences 
in  the  temperatures  which  prevail  at  different  heights.  Stoves  of 
cast-iron,  too,  at  red  heat  permit  the  passage  of  gases,  especially 
hydrogen  and  carbon  monoxide,  the  latter  of  which  exercises 
poisonous  effects  on  the  occupants  of  the  room.  Stoves  of  sheet- 
iron  or  porcelain  are  far  preferable  as  regards  this  defect. 

Warming  by  Hot  Air. — This  method  of  warming  also  depends 
upon  the  dilation  and  rarefaction  of  air  by  heat.  In  this  method 
the  external  air  is  led  into  a  chamber  heated  by  a  furnace,  or  it 
may  be  that  the  air  in  the  chamber  is  made  to  pass  over  pipes 
heated  by  water  or  steam.  From  this  heating  chamber  conduct- 
ing channels  or  pipes  lead  to  the  apartments  to  be  heated. 

Ventilation. — Many  of  the  most  successful  methods  of  venti- 
lation depend  upon  these  same  principles  of  rarefaction  by  heat,  the 
general  idea  being  to  produce  at  some  point  an  upward  current  of 
air  by  heat  and  then  have  pure  air  introduced  to  takes  its  place. 
The  upward  draught  should  be  arranged  to  carry  off  the  foul  air 
and  to  produce  a  complete  renovation  of  the  air  of  the  space  to  be 
ventilated.  From  what  has  been  said  it  is  evident  that  some  of 
the  methods  of  heating  accomplish  a  more  or  less  perfect  venti- 
lation, especially  the  open  fireplace.  In  general,  however,  in  work- 
shops and  large  buildings  other  special  arrangements  have  to  be 
resorted  to.  In  private  dwellings  chimneys  are  very  beneficial 


26  ELEMENTARY  LESSONS  IN  HEAT. 

ventilators,  with  or  without  fires.  Iii  mines  this  method  of  venti- 
lating by  draught  is  frequently  adopted.  By  building  fires  at  the 
bottom  of  one  or  more  shafts,  ascending  columns  of  air  are  pro- 
duced, and  fresh  air  is  admitted  at  other  points  and  made  to 
circulate  through  the  different  compartments  of  the  mine  before 
it  can  reach  these  exit  shafts.  Ventilation  is  also  accomplished 
by  mechanically  forcing  air  through  the  compartments  to  be  venti- 
lated. 


CHAPTER  III. 
CALORIMETRY. 

As  has  already  been  stated,  heat  produces  effects  of  various 
kinds  on  bodies:  it  usually  changes  the  temperature,  generally 
alters  the  volume  and  pressure,  and  sometimes  changes  the  state 
of  a  body  from  a  solid  to  a  liquid,  or  a  liquid  to  a  gas. 

Calorimetry  has  for  its  object  the  measurement  of  quantities  of 
heat,  and  any  of  the  measurable  effects  of  heat  may  be  used  for 
that  purpose;  the  most  convenient,  however,  is  the  alteration  of 
temperature  produced  in  a  known  weight  of  a  given  substance  by 
the  communication  or  abstraction  of  the  heat  to  be  measured. 

Unit  of  Heat. — In  estimating  quantity  of  heat  by  the  change 
of  temperature  it  produces,  the  unit  of  heat,  or  thermal  unit,  is 
taken  as  the  amount  of  heat  necessary  to  raise  a  unit  mass  of  water, 
taken  at  a  standard  temperature,  through  one  degree  centigrade. 
Since  the  unit  of  mass  is  not  the  same  in  all  countries,  the  thermal 
unit  also  varies.  In  this  text  the  pound  measures  the  unit  of 
mass. 

There  is  no  general  agreement  as  to  the  standard  temperature 
at  which  the  water  is  to  be  taken,  but  we  shall  suppose  this  standard 
temperature  to  be  15.5°  C.  or  60°  F. 

Necessary  Principles. — The  calorimetrical  measurements  most 
necessary  to  be  made  are  those  for  determining  the  quantities  of 
heat  given  off  or  absorbed  by  bodies  when  their  temperatures 
change  through  certain  intervals  or  when  they  change  their  states 
of  aggregation.  "We  are  here  concerned  with  the  former. 

1st.  All  that  is  assumed  in  these  measurements  is  that,  if  it 
takes  a  certain  quantity  of  heat  to  produce  a  certain  temperature 
effect  in  a  given  portion  of  a  homogeneous  substance,  the  same 
amount  of  heat  will  produce  the  same  effect  in  another  equal  por- 

27 


28  ELEMENTARY  LESSONS  IN  HEAT. 

tion,  or  that  the  heat  required  to  raise  the  temperature  of  two 
pounds  of  a  substance  through  a  certain  interval  is  twice  as  great 
as  that  required  to  raise  one  pound  of  the  same  substance  through 
the  same  interval. 

2d.  Another  principle  employed,  the  truth  of  which  is  estab- 
lished by  experiment,  is  that  the  heat  given  to  a  body  to  cause  it  to 
pass  through  a  series  of  states,  as  regards  temperature  and  volume, 
is  the  same  as  that  given  out  by  the  body  in  cooling  and  passing  in 
reverse  order  through  the  same  states. 

We  cannot,  however,  assume  that  the  quantities  of  heat  re- 
quired to  raise  the  temperature  of  a  body  through  equal  intervals 
are  always  the  same,  for  it  may  require  a  different  amount  of  heat 
to  raise  the  temperature  of  the  body  from  5°  to  10°  than  from  40° 
to  45°. 

Thermal  Capacity. — If  a  quantity,  Q,  of  heat  be  taken  from  or 
given  to  a  body  and  produce  in  it  a  change  of  temperature  t°, 

then  y-  is  called  the  mean  thermal  capacity  of  the  body  between  the 

initial  and  final  temperature. 

From  the  definition  of  the  unit  of  heat  it  is  evident  that  the 
thermal  capacity  of  a  quantity  of  cold  water  is  "numerically  equal 
to  its  mass  expressed  in  pounds;  and  the  thermal  capacity  of  any 
other  body  is  numerically  equal  to  the  weight  of  water,  in  pounds, 
which  would  have  the  same  thermal  capacity.  This  quantity  of 
water  is  also  called  the  water  equivalent  of  the  body. 

Specific  Heat. — In  the  above  expression  -~9  if  the  unit  of  mass 

be  taken  and  t  =  1,  the  expression  indicates  the  thermal  capacity 
of  the  unit  of  mass,  or  the  specific  heat  of  the  body.  We  may 
define  the  specific  heat  of  a  body  as  the  amount  of  heat,  expressed 
in  thermal  units,  whicli  must  be  transferred  to  or  from  a  unit 
mass  of  the  body,  taken  under  specific  conditions,  in  order  to  raise 
or  loiver  its  temperature  one  degree. 

From  what  precedes,  it  is  evident  that  m  pounds  of  a  substance 
in  changing  its  temperature  through  t  degrees  will  take  up  or  give 
out  a  quantity  of  heat  equal  to  mst,  where  s  denotes  the  mean 
specific  heat  of  the  body  between  the  initial  and  final  temperatures. 


OAL  ORIMETR  T.  29 

Determination  of  Specific  Heat. — By  Mixtures. — Let  us  take  a 
known  weight  m  of  a  substance  whose  specific  heat  is  desired,  and 
heat  to  a  known  temperature  t,  and  then  mix  it  with  a  known 
weight  n  of  water  at  a  lower  known  temperature  t',  at  or  near  zero. 
If  we  suppose  thai  there  is  no  external  loss  or  gain  of  heat,  we 
have  a  means  of  determining  specific  heat,  for  the  heat  taken  from 
the  hot  body  is  given  to  the  water;  and  if  we  let  6  denote  the 
common  temperature  first  reached  by  the  mixed  liquids,  and  x  the 
required  specific  heat,  we  shall  have 

mx(t  -  B)  =  n(B  -  t'), 

from  which  x  becomes  known. 

This  method  is  applicable  to  the  case  of  any  two  bodies  at  dif- 
ferent temperatures  that  can  be  brought  to  the  same  temperature 
by  an  interchange  of  heat  between  themselves  only,  even  though 
literal  mixing  cannot  be  accomplished.  Thus  a  solid  may  be  im- 
mersed in  a  liquid.  Nor  is  it  necessary  to  use  only  water:  any 
liquid  whose  specific  heat  is  known  may  be  used. 

This  method,  though  convenient,  is  not  accurate,  for  the  theo- 
retical conditions  assumed  cannot  be  realized,  and  there  must  be 
some  external  loss  or  gain  of  heat. 

Method  of  Melting  Ice. — The  determination  of  specific  heat  by 
this  method  consists  in  finding  the  amount  of  ice,  at  the  freezing 
point,  melted  by  a  known  weight  of  a  substance,  heated  to  a  known 
temperature.  If  the  amount  of  heat  necessary  to  convert  ice  into 
water  is  known,  we  can  then  find  the  specific  heat  of  the  body 
operated  upon. 

Method  of  Cooling. — Specific  heat  may  also  be  estimated  by  com- 
paring the  times  the  bodies  occupy  in  cooling  through  the  same 
number  of  degrees. 

In  the  following  table  are  given  the  average  specific  heats  of  the 
substances  named,  between  15°  C.  and  98°  0.,  as  determined  by 
Kegnault : 


Water 1.0080 

Charcoal 0-2414 

Aluminium 0.2143 

Sulphur  (native) 0.1776 

Iron 0.1138 

Nickel 0.1086 

Zinc..  ..  0.0955 


Copper 0.0952 

Silver 0.0570 

Tin 0.0562 

Mercury 0  0333 

Platinum 0.0329 

Gold 0.0324 

Lead .  0.0314 


30  ELEMENTARY  LESSONS  IN  HEAT. 

In  general,  the  specific  heats  of  solids  and  liquids  increase  as 
the  temperature  rises,  and  the  specific  heat  of  a  body  in  the  liquid 
state  is  greater  than  in  the  solid.  With  solids  there  is  generally 
found  a  decrease  of  specific  heat  with  an  increase  of  density. 

Great  Specific  Heat  of  Water. — No  solid  or  liquid  substance 
(with  one  exception*)  has  been  found  to  have  as  great  a  specific 
heat  as  water;  and  among  the  gases  whose  specific  heats  have  been 
determined,  that  of  hydrogen  alone  exceeds  that  of  water.  The 
specific  heats  of  ice  and  steam  are  about  one-half,  and  that  of  the 
atmosphere  and  the  solid  parts  of  the  earth's  crust  about  one-fourth, 
that  of  water.  With  the  two  exceptions  named,  water,  therefore, 
absorbs  or  emits  in  its  changes  of  temperature  more  heat  than  other 
substances  that  have  been  experimented  upon.  The  quantity  of 
heat  required  to  raise  a  pound  of  water  from  0°  to  100°  0.  is  suffi- 
cient to  raise  thirty  pounds  of  mercury  through  the  same  interval, 
and  would  raise  one  and  two- third 3  pounds  of  silver  from  0°  to  the 
fusing  point,  1037°  C.  It  will  be  found  that  this  property  of  water 
plays  an  important  part  in  nature,  and  is  frequently  utilized  for 
heating  buildings  and  for  other  domestic  purposes. 

Specific  Heat  of  Gases. — The  determination  of  the  specific  heat 
in  the  case  of  gases  is  attended  with  greater  difficulty  than  in  the 
case  of  solids  and  liquids,  both  from  an  experimental  and  a  theo- 
retical point  of  view.  The  measurement  of  the  specific  heat  of  a 
gas  may  be  made  either  at  a  constant  pressure  or  a  constant  volume; 
the  specific  heat  at  a  constant  pressure  is  always  the  greater;  the 
two  specific  heats  are  simply  connected  in  the  case  of  perfect  gases. 
The  experiments  of  Regnault  established  the  following  facts  in 
regard  to  gases : 

1st.  The  specific  heat  of  a  given  weight  of  the  more  permanent 
gases  does  not  vary  with  the  temperature  or  density  of  the  gas. 
The  specific  heat  of  a  given  volume  of  such  gas  accordingly  varies 
as  its  density. 

2d.  Equal  volumes  of  the  more  non-condensable  elementary 
gases  have  the  same  specific  heats,  when  compared  under  the  same 
temperature  and  pressure. 

*  The  experiments  of  Dupre  (Phil.  Trans.  1869)  appear  to  prove  pretty  con- 
clusively that  the  specific  heat  of  a  mixture  of  alcohol  and  water  is  greater  than 
that  of  water,  until  the  mixture  reaches  a  strength  of  36  per  cent,  of  alcohol. 


CALORIMETRY. 


31 


The  specific  heat  of  carbon  dioxide  was  found  to  vary  with  the 
temperature,  and  only  oxygen,  hydrogen,  and  nitrogen  among  the 
elementary  gases  conformed  to  the  second  law. 

The  following  table  gives  the  specific  heats  of  the  gases  named, 
according  to  Kegnault,  pressure  being  constant  and.  the  specific 
heat  of  water  taken  as  unity : 

For  equal     •-..-••         or  equal 
Weights.  Volumes. 

Atmospheric  air 0.2377  0.2374 

Oxygen 0.2175  0.2405 

Nitrogen 0.2438  0.2368 

Hydrogen 3.4090  0.2359 

Aqueous  vapor 0.4805  0.2989 

Carbon  monoxide 0.2450  0.2370 

Carbon  dioxide 0.2169  0.3307 

Olefiant  gas 04040  0.4160 

Marsh  gas  0.5929  0.3277 

Ammonia  gas 0.5084  0.2996 

The  volumes  of  the  gases  are  referred  to  an  equal  volume  of  air, 
the  specific  heat  of  the  volume  of  air  being  referred  to  an  equal 
weight  of  water. 

The  specific  heat  of  a  body  in  a  liquid  state  is  generally  greater 
than  that  of 'the  same  body  in  either  the  solid  or  the  gaseous  state. 
The  following  table  shows  this  relation  between  the  specific  heats 
of  the  substances  named  in  the  different  states — temperature  given 
on  Fahrenheit  scale: 


SOLID. 

LIQUID. 

G, 

us. 

SUBSTANCE. 

Specific 
Heat. 

Temperature. 
Between 

Specific 
Heat. 

Temperature. 
Between 

Specific 
Heat. 

Temper- 
ature. 
Above 

Ice  

0.5050 

—  22°and  +  323 

1.0000 

32°  and   68° 

0.4805 

212° 

Bromine.  . 
Tin  

0.0843 
0.0562 

-108°  and  -    4° 
32°  and    212° 

0.1060 
00637 

10°  and  118° 
482°  and  662° 

0.0555 

Lead  . 

0  0314 

32°  and    212° 

0  0402 

662°  and  842° 

Alcohol... 
Carbon  bi- 
sulphide. 
Ether  

0.5475 

0.2352 
0  5290 

0.4534 

0.1569 
0.4797 

CHAPTER  IV. 
PRODUCTION  AND  CONDENSATION  OF  VAPOR. 

Vaporization. —  Vaporization  is  a  general  term  applied  to  any 
process  by  which  a  liquid  is  converted  into  a  vapor.  When  the 
change  takes  place  from  the  surface  without  visible  disturbance 
of  the  liquid,  it  is  called  evaporation.  Under  ordinary  atmospheric 
conditions  most  liquids  undergo  this  change.  Evaporation  does 
not  occur  at  a  particular  temperature  only,  but  takes  place  over 
a  wide  range  of  temperature.  At  very  low  temperatures  evapora- 
tion is  insensible  for  many  substances,  if  it  takes  place  at  all. 

Some  solids  change  to  the  vaporous  state  without  passing 
through  the  liquid  state :  in  these  cases  the  process  is  called  subli- 
mation. Ice,  snow,  and  camphor  are  examples. 

Vapors  and  gases  are  the  terms  used  to  designate  the  aeriform 
bodies  into  which  liquids  pass  by  vaporization.  The  distinction,  as 
the  terms  are  generally  employed,  is  that  gases  are  vapors  more 
difficult  to  condense,  and  under  ordinary  conditions  are  always 
aeriform,  while  vapors  may  exist  under  ordinary  conditions  as  solids 
or  liquids.  A  more  exact  distinction  will  appear  later,  p.  38. 

Vapors,  thus  limited,  under  ordinary  conditions  have  properties 
such  that  it  is  necessary  to  consider  them  separately  from  gases. 
The  formation  of  vapors  and  their  elastic  force  are  subjects  of  much 
importance. 

Maximum    Pressure   and  Density   of  Vapors  in  Vacuo. — The 

elastic  force  and  other  properties  of  a  vapor  may  be  observed  in 
such  an  arrangement  as  is  shown  by  Fig.  17.  A  glass  globe  is  con- 
nected by  a  rubber  tube  with  a  U-shaped  glass  tube  containing 
mercury,  called  a  manometer.  The  air  is  first  exhausted  from  the 
globe  and  its  tube-connection.  Of  course,  the  mercury  ascends  in 
the  left  and  descends  in  the  right  branch  of  the  glass  tube  as  the 
exhaustion  is  perfected;  if  all  the  air  is  taken  from  the  globe,  the 
level  of  the  mercury  in  the  two  tubes  will  differ  by  the  height  01  the 
'  32 


PRODUCTION  AND   CONDENSATION  OF   VAPOR. 


33 


barometer  column.  A  little  liquid  is  then  admitted  into  the  globe 
through  the  stopcock  R,  which  is  so  arranged  as  to  admit  the  liquid 
without  admitting  air. 

As  soon  as  the  liquid  is  passed  through  the  stopcock  the 
mercury  in  the  left  branch  of  the  manometer  descends,  and,  as  no 
liquid  appears  in  the  globe,  we 
conclude  that  the  liquid  is  im- 
mediately converted  into  vapor, 
and  that  the  vapor  presses 
down  the  mercury.  As  we  con- 
tinue to  introduce  the  liquid 
the  mercury  column  descends 
more  and  more,  but  finally  it 
ceases  to  descend,  and  any  ad- 
ditional liquid  introduced  will 
be  left  u  n  evaporated  in  the  tube 
attached  to  the  globe. 

If  now  the  temperature  of 
the  globe  be  increased,  more  of 
the  liquid  will  be  evaporated 
and  a  greater  pressure  indi- 
cated by  the  manometer.  Fur- 
ther experiment  will  continue 
to  show  that  the  amount  of  the 
liquid  evaporated  and  the  press- 
ure exerted  will  depend  upon 
the  temperature  of  the  space. 
We  are  thus  enabled  to  con- 
clude that  the  amount  of  vapor 
which  passes  from  a  liquid  in 
vacua  and  the  pressure  exerted 
by  the  vapor  in  a  given  space 
are  limited,  and  vary  with  the 
temperature.  This  pressure  of 

the  vapor  in  contact  with  its  liquid,  being  the  greatest  possible  for 
the  temperature,  is  called  its  maximum  pressure,  and  under  such 
conditions  the  space  is  said  to  be  saturated. 

The  maximum  density  for   any  temperature    is  that  state  of 
density  which  the  vapor  cannot  exceed  without  becoming  liquid 


FIG.  17.— VAPOR  DENSITY  AND  PRESSURE. 


34 


ELEMENTARY  LESSONS  IN  HEAT. 


It  can  be  shown  that  the  vapor  of  a  saturated  space  is  at  its  maxi- 
mum density  because  it  is  impossible  to  diminish  the  volume 
occupied  by  the  vapor  without  liquefying  a  portion  of  it.  If  the 
vapor  be  not  at  its  maximum  density  and  its  volume  be  decreased, 
temperature  remaining  constant,  an  increase  of  pressure  and  den-> 
sity  will  take  place  until  the  point  of  maximum  density  is  reached. 
These  effects  of  change  of  volume  may  be 
roughly  illustrated  by  having  a  barometer- 
tube,  with  the  usual  vacuous  space  above  the 
mercury,  inverted  in  a  deep  cistern  of  mer- 
cury, as  shown  in  Fig.  18.  Let  a  small 
amount  of  ether,  not  sufficient  to  saturate 
the  vacuous  space,  be  introduced  into  the 
tube.  The  column  of  mercury  will  descend, 
due  to  the  elastic  force  of  the  vapor.  If  we 
now  shove  the  tube  down  into  the  cistern,  we 
shall  see  the  mercury  descend  more,  due  to 
the  increased  elastic  force  of  the  vapor,  while 
the  volume  occupied  by  the  vapor  decreases, 
and  its  density  accordingly  increases.  The 
reverse  effect  is  observed  if  the  tube  be  lifted 
up.  After  the  tube  has  been  shoved  down 
a  certain  distance,  the  mercury  column  no 
longer  descends,  showing  that  the  pressure  of 
the  vapor  does  not  increase.  As  soon  as  this 
point  is  reached,  liquid  ether  appears  on  the 
surface  of  the  mercury.  We  then  know  that 
the  space  above  the  mercury  is  saturated. 
So  long  as  this  is  the  case  it  matters  not 
whether  we  raise  or  depress  the  tube  ;  the 
height  of  the  mercurial  column  is  constant, 
showing  that  the  pressure  of  the  saturated 
vapor  remains  constant  in  the  two  cases. 

It  has  been  seen  that  the  maximum  den- 
FIQ.  is.— EFFECT  OF  PRESS-    ^    an(j   pressure   are  dependent  upon  the 

URE  ON  ETHER  VAPOR.  •>  . «. 

temperature,   and    increase    rapidly  as   the 

temperature  rises.  In  order,  therefore,  to  saturate  a  given  space, 
a  greater  quantity  of  vapor  is  required  as  the  temperature  rises. 
This  is  illustrated  in  the  case  of  water  vapor  by  the  following  table, 


PRODUCTION  AND  CONDENSATION  OF  VAPOR. 


35 


in  which  is  given  the  elastic  pressure  of  such  vapor  at  saturation  at 
different  temperatures,  with  the  corresponding  weights  contained 
in  a  cubic  foot  of  saturated  space. 

Weight  of  Vapor 
in  cubic  foot  in  grains. 

.045  0.54 

.071  0.84 

.109 

.167 

.246 


Temperature  F. 
0° 
10° 
20° 
30° 
40° 
50° 
60° 
70° 
90° 
100° 


Elastic  Pressure 
In  inches  of  barometer. 


.517 

.732 

1.407 

1.913 


1.30 
1.97 
2.86 
4.09 
5.76 
7.99 
14.81 
19.79 


Vapor  which  is  at  less  than  its  maximum  density  is  called 
superheated  vapor,  because  it  can  be  obtained  by  heating  vapor  at 
maximum  density  at  lower  temperature. 

Fig.  19  represents  graphically  the  rate  at  which  the  maximum 
density  of  aqueous  vapor  increases  with  the  temperature  between 


—  20° 


— 10°  0°  + 10° 

FIG.  19.— CURVE  OF  VAPOR  DENSITY. 


a  and  b.  The  horizontal  distances  proportional  to  temperature  are 
laid  off  on  the  base  line  ab,  and  the  corresponding  vertical  lines  at 
every  fifth  degree  are  proportional  to  the  masses  of  vapor  necessary 
to  saturate  the  spaces  at  the  temperatures.  It  is  noticed  that  the 
curve,  ac,  of  vapor  density  becomes  steeper  as  the  temperature  in- 


36  ELEMENTARY  LESSONS  IN  HEAT. 

creases,  showing  that  the  amount  of  vapor  for  saturation  increases 
more  rapidly  at  high  than  at  low  temperature. 

No  general  formula  has  been  deduced  which  will  express  the 
relation  between  the  pressures  and  temperatures  in  the  case  of 
saturated  vapors.  The  many  experiments  on  saturated  aqueous 
vapor,  the  most  celebrated  of  which  are  Regnault's,  have  suggested 
numerous  empirical  formulae  which  may  be  used  for  that  purpose 
in  the  case  of  steam.  As  nearly  all  recent  works  on  steam  give 
tables  showing  ,the  relations  between  pressures,  temperatures,  and 
volumes,  such  formulae  are  now  seldom  necessary. 

Mixture  of  Gas  and  Vapor  in  a  Confined  Space. — If  the  experi- 
ment with  the  apparatus  (Fig.  17)  be  repeated  without  exhausting 
the  air,  the  results  finally  obtained  are  the  same  as  with  the  ex- 
hausted receiver.  . 

The  only  effect  of  the  air  is  to  retard  the  production  of  the 
vapor,  but  the  evaporation  goes  on  until  the  pressure  is  the  maxi- 
"mum  pressure  due  to  that  temperature.  The  more  dense  the  gas 
which  is  present,  the  greater  the  retardation.  In  vacuo  the  vapor 
passes  very  rapidly  to  the  state  of  maximum  density.  The  above 
deductions  were  given  by  Dalton  in  two  laws,  which  may  be  stated 
as  follows : 

1st.  The  quantity  of  vapor  which  can  be  contained  in  a  given 
space,  or  the  ultimate  pressure  of  a  saturated  vapor,  is  dependent 
only  on  the  temperature.  It  is  the  same  whether  or  not  the  space 
contain  other  gas. 

2d.  When  a  space  containing  other  gas  is  saturated  with  vapor, 
the  pressure  of  the  mixture  is  the  sum  of  the  pressure  due  to  the 
vapor  and  the  gas  separately. 

This  second  law  applies  whether  the  vapor  be  saturated  or  not, 
and  is  a  particular  case  of  the  more  general  law, — that  each  gas  in 
a  mixture  of  gases  and  vapors  exerts  in  a  confined  space  the  same 
pressure  as  if  the  others  were  absent. 

It  may  be  well  to  here  state  again  directly  the  following  infer- 
ences from  the  facts  of  the  above  paragraphs.  The  greatest  pres- 
sure and  density  that  a  vapor  can  have  at  any  temperature  is  when 
it  is  in  a  state  of  saturation  for  that  temperature.  Vapors  in  contact 
with  their  liquids  in  a  confined  space  soon  pass  to  saturation,  for 
the  temperature  and  any  diminution  of  volume  by  increase  of  ex- 


PRODUCTION  AND  CONDENSATION  OF  VAPOR.  37 

ternal  pressure,  or  any  decrease  of  temperature,  will  cause  conden- 
sation of  a  part  of  the  vapor. 

Condensation  of  Vapors. — 1.  Since  a  vapor  in  the  saturated  state 
is  at  its  maximum  density  for  the  temperature,  it  is  evident  that,  if 
the  volume  of  such  vapor  be  decreased  without  change  of  tempera- 
ture, a  portion  of  the  vapor  corresponding  to  the  decrease  of  volume 
will  be  condensed,  and  the  remaining  portion  will  be  at  the  maxi- 
mum density  and  pressure. 

2.  Since  the  maximum  density  and  pressure  of  a  vapor  in  a  con- 
fined space  depend  only  upon  the  temperature,  if  the  temperature 
of  a  saturated  space  be  lowered  and  the  volume  kept  constant,  both 
density  and  pressure  of  the  vapor  will  fall  to  correspond  to  the  lower 
temperature,  and  as  much  vapor  will  be  condensed  as  corresponds 
to  the  difference  of  maximum  density  at  the  two  temperatures. 

It  is  thus  seen  that  both  extraneous  pressure  and  reduction  af 
temperature  are  effective  in  condensing  vapors,  and  they  may  be 
employed  separately  or  conjointly.  The  same  means  are  employed 
in  the  condensation  of  gases. 

Critical  Temperatures. — Andrews  was  the  first  to  show  that 
there  probably  exists  for  each  gas  or  vapor  a  temperature  above 
which  no  amount  of  pressure  can  liquefy  it :  this  temperature  is 
called  the  critical  temperature. 

Below  the  critical  temperature  sufficient  external  pressure  will 
bring  the  vapor  to  its  maximum  density,  after  which  further  dimi- 
nution of  volume  will  liquefy  it  without  increase  of  its  pressure,  as 
already  pointed  out. 

Continuity  of  Liquid  and  Gaseous  State. — Below  their  critical 
temperatures,  under  sufficient  pressure,  all  gases  and  vapors  are 
liquid;  above  that  temperature  they  are  gaseous;  and  if  the  pressure 
be  kept  up  between  the  two  temperatures  the  transition  is  unrecog- 
nizable. 

All  ordinary  liquids  have  their  critical  temperatures,  above 
which  no  amount  of  pressure  will  keep  them  in  the  liquid  state. 

The  critical  temperature  of  hydrogen  is  believed  to  be  about 
—  204°  C.,  while  that  of  chlorine  is  +  140°  C.  The  critical  tem- 
perature of  water  vapor  is  still  much  higher,  approaching  a  low  red 


Liquefaction  and  Solidification  of  Permanent  Gases. — Until  1877 
a  number  of  gases  had  resisted  all  attempts  to  liquefy  them,  and 


38  ELEMENTARY  LESSONS  IN  HEAT. 

hence  were  designated  as  permanent  gases,  among  which  were 
oxygen,  hydrogen,  and  nitrogen.  In  the  latter  part  of  1877  and 
the  first  part  of  1878  oxygen  was  also  liquefied  by  combining  great 
pressure  with  great  cold.  This  result  was  accomplished  at  about 
the  same  time  by  Cailletet,  of  France,  and  Pictet,  of  Switzerland, 
acting  independently  of  each  other,  and  thus  verified  Andrews's  law 
as  to  critical  temperature.  Pictet  thought  that  he  had  succeeded  in 
liquefying  hydrogen  also,  but  it  is  now  believed  that  he  was  mis- 
taken. This  gas  has  now  been  liquefied,  the  temperature  em- 
ployed being  below  —  205°  C.  Nitrogen  has  also  been  liquefied,  its 
critical  temperature  being  —  146°  C.  The  critical  temperature  of 
oxygen  is  — 113°  C.  Both  oxygen  and  nitrogen  have  been  solidified. 
When  near  their  condensing  points  these  gases,  like  vapors,  depart 
widely  from  the  laws  of  Boyle  and  Charles. 

These  considerations  furnish  us  with  a  basis  for  a  slight  distinc- 
tion between  gases  and  vapors.  Below  the  critical  temperature  the 
substance  is  a  vapor,  above  the  critical  temperature  a  gas.  In  the 
latter  condition  it  obeys  very  nearly  the  laws  of  Boyle  and  Gay- 
Lussac  until  greatly  compressed ;  in  the  form  of  vapor  it  departs 
more  widely  from  these  laws. 

Conditions  Affecting  Rapidity  of  Evaporation. — Some  substances 
evaporate  much  more  rapidly  than  others,  and  are  then  said  to  be 
more  volatile;  for  instance,  alcohol  and  ether  evaporate  much  more 
rapidly  than  water.  The  rapidity  of  evaporation  is  subject  to  the 
following  laws: 

1st.  It  increases  directly  with  the  temperature  and  with  the  ex- 
tent of  evaporating  surface. 

2d.  It  increases  the  more  nearly  the  evaporation  takes  place  in 
a  vacuum. 

3d.  It  increases  with  the  rapidity  with  which  the  vapor  is  re- 
moved from  over  the  liquid. 

The  third  law  is  evidently  a  consequence  of  the  second,  and  both 
the  second  and  third  flow  from  principles  stated  in  the  paragraphs 
relating  to  the  pressure  and  density  of  vapor. 

The  evaporation  of  water  takes  place  on  an  enormous  scale  in 
nature,  and  supplies  the  moisture  to  the  air  which  again  descends 
as  rain.  Without  this  circulation  the  present  conditions  of  life 
could  not  prevail. 


PRODUCTION  AND   CONDENSATION  OF  VAPOR.  39 

Besides  this  quiet  transformation  into  the  vaporous  state,  which 
has  been  called  evaporation,  there  are  other  forms  of  vaporization 
which  we  will  now  describe. 

Ebullition  or  Boiling.— When  a  liquid  is  heated  in  an  open 
vessel,  the  evaporation  first  goes  on  quietly  and  the  liquid  steadily 
rises  in  temperature.  After  a  time  very 
minute  bubbles  are  given  off :  these  are 
bubbles  of  air.  Soon  after,  at  the  bottom 
of  the  vessel  and  at  other  parts  most  ex- 
posed to  the  heat,  bubbles  of  vapor  are 
formed  and  ascend,  decreasing  in  size  as 
they  move  upward,  and  disappear  before 
reaching  the  surface,  being  condensed  by 
the  colder  upper  layers  of  water.  The  col- 
lapsing of  these  bubbles  produces  the  sing- 
ing of  liquids  before  they  boil.  Finally  the 
bubbles  increase  in  number  and  grow  larger 
as  they  ascend  until  they  burst  at  the  sur-  Fia  20-BoiLING 
face.  The  liquid  is  thus  kept  agitated  and  gives  off  vapor  much 
faster  ;  it  is  then  said  to  boil  or  be  in  a  state  of  ebullition.  These 
phenomena  may  be  readily  observed  in  a  glass  vessel  such  as  is  rep- 
resented in  Fig.  20. 

Laws  of  Ordinary  Ebullition. — Experiment  enables  us  to  state 
the  following  laws  of  ebullition  : 

1st.  Under  the  same  pressure  there  is  a  definite  boiling  point 
for  every  liquid.  The  boiling  point  is  then  a  specific  property  of 
the  liquid,  and  is  a  physical  character  of  importance  in  distinguish- 
ing liquids  which  otherwise  resemble  each  other. 

The  following  table  gives  the  boiling  points  of  the  liquids  named, 
under  common  atmospheric  pressure  : 

Ammonia —34°  C. 

Common  ether 87° 

Carbon  bisulphide 48° 

Alcohol c 79° 

Distilled  water 100* 

Turpentir  e 130° 

Glycerin 290° 

Sulphuric  acid  (concentrated) „ 338° 

Mercury 357C 


40 


ELEMENTARY  LESSONS  IN  HEAT. 


a 


2d.  When  ebullition  has  commenced  the  temperature  of  the 
liquid  remains  constant  (pressure  constant),  however  much  heat  be 
applied. 

The  liquid  must  be  kept  thoroughly  stirred,  to  avoid  small 
fluctuations  of  temperature  The  temperature  of  the  vapor  is  more 

constant,  than  that  of  the  liquid  ; 
hence  with  water  we  employ  the 
vapor  in  determining  the  boiling 
point  on  the  thermometer.  The  con- 
stancy of  temperature  during  ebul- 
lition explains  why  vessels  of  easily 
fusible  metal  may  be  exposed  to  the 
action  of  a  hot  fire  provided  they 
contain  water,  for  they  cannot  be 
heated  much  above  100°  until  the 
water  has  evaporated.  That  the 
temperature  remains  constant  during 
ebullition,  notwithstanding  the  con- 
tinued application  of  heat,  will  be  ex- 
plained subsequently. 

3d.  The  pressure  of  the  vapor 
given  off  during  ebullition  is  equal  to 
that  of  the  external  medium. 

This  law  has  been  verified  in  the 
case  of  the  atmosphere  by  a  very 
simple  arrangement,  shown  in  Fig. 
21.  A  barometer-tube  is  bent,  near 
the  closed  end,  to  a  U -shape.  The 
shorter  limb  of  the  tube  is  filled  with 
mercury,  except  a  small  space  occu- 
pied by  water.  The  mercury  extends 
around  the  bend  a  little  way  up  the 
longer  branch.  Under  ordinary  con- 
ditions the  mercury  in  the  shorter 
limb  will  stand  higher  than  that 
in  the  other.  But  let  the  water 
in  the  shorter  limb  be  brought  to  the  boiling  temperature  by  im- 
mersing the  tube  in  the  steam  from  boiling  water,  as  shown  in 
Fig.  21.  The  steam  from  the  water  in  the  shorter  limb  presses  the 
mercury  down  until  its  level  is  the  same  in  both  limbs,  showing 


FIG.  21.— VAPOR  PRESSURE  FROM 
BOILING  WATER. 


PRODUCTION  AND   CONDENSATION  OF  VAPOR. 


41 


that  the  pressure  in  the  shorter  limb  is  exactly  equal  to  the  atmos- 
pheric pressure  in  the  longer  limb. 

Boiling  Point. — A  liquid  is  in  ebullition  when  it  gives  off  vapor 
at  the  same  pressure  as  that  to  which  the  free  surface  of  the  liquid 
is  exposed ,  and  the  boiling  point  is  the  lowest  temperature  at  which 
ebullition  can  occur. 

In  ebullition  the  elastic  bubbles  of  vapor  formed  below  the  sur- 
face of  the  liquid  have  to  withstand  the  weight  of  the  liquid  above 
them  and  the  pressure  of  the  atmosphere.  In  order  to  escape  from 
the  liquid  they  must  in  addition  overcome  the  cohesion  of  the  liquid 
and,  at  the  sides,  the  adhesion  to  the  vessel.  The  first  element  of 
pressure  diminishes  as  the  bubble  rises,  and  at  the  surface  of  the 
liquid  the  pressure  to  which  it  is  subjected  is  reduced  to  that  of  the 
atmosphere.  There  is  thus  evidently  a  greater  pressure  on  the 
bubbles  of  vapor  formed  lowest  in  the  liquid.  From  these  consid- 
erations we  can  anticipate  several  means  of  varying  the  boiling 
point :  the  most  evident  is  by  pressure. 

Effect  of  Pressure  on  the  Boiling  Point. — Ebullition,  like  fu- 
sion, under  constant  pressure,  commences  and  continues  at  a  constant 
temperature.  As  all  substances  increase  in  vol- 
ume upon  vaporization,  we  should  expect  that 
increase  of  pressure  would  raise  the  boiling 
point,  and  the  reverse,  and  experiment  shows 
this  to  be  the  case.  Water  may  be  made  to 
boil  at  any  temperature  between  0°  and  100° 
by  sufficiently  diminishing  the  pressure  to 
which  it  is  subjected.  The  boiling  point  of 
water  is  associated  in  our  minds  with  a  fixed 
temperature  because  it  usually  boils  under 
atmospheric  pressure,  and  the  variations  of 
atmospheric  pressure  are  comparatively  small. 
It  is  also  evident  from  the  foregoing  that  there 
is  a  slight  difference  of  temperature  in  the 
different  layers  of  the  same  liquid,  owing  to  FIG.  22. -BALING  nTc^D. 
difference  of  pressure. 

Dimi/iished  Pressure  Illustrated. — A  little  water  is  boiled  over 
&  lamp  in  a  glass  flask  until  the  air  is  driven  out.  A  closely-fitting 
cork  is  then  inserted,  and  at  the  same  time  the  lamp  removed. 


42  ELEMENTARY  LESSONS  IN  HEAT. 

When  ebullition  has  ceased,  it  may  be  renewed  for  a  considerable 
time  by  pouring  cold  water  on  the  flask  above  the  liquid.  A  Flor- 
ence flask  is  very  convenient,  and  may  be  inverted  when  removed 
from  the  lamp  and  held  by  the  neck,  as  in  Fig.  22.  The  cold  water 
condenses  the  vapor  above  the  liquid  and  thus  diminishes  the  pres- 
sure upon  it.  In  this  experiment  a  fragile  vessel  is  likely  to  be 
crushed  when  the  vapor  is  condensed.  The  experiment  is  often 
called  the  culinary  paradox. 

On  the  other  hand,  by  increasing  the  pressure  on  the  free  sur- 
face of  the  liquid,  by  its  own  vapor  or  otherwise,  the  boiling  point 
may  be  raised  at  pleasure. 

Other  Causes  Affecting  the  Boiling  Point. — 1.  The  nature  of 
the  vessel  also  influences  the  boiling  point ;  the  boiling  point  is  dif- 
ferent in  metallic  and  glass  vessels,  being  higher  in  the  glass.  In 
this  case  the  water  may  be  heated  to  105°  or  106°  without  boiling ; 
then  there  is  a  violent  escape  of  steam,  and  the  temperature  of  the 
water  falls  nearly  to  the  normal  boiling  point,  and  remains  tranquil 
until  the  temperature  again  rises  and  the  phenomenon  repeats  it- 
self. This  intermittent  formation  of  vapor  produces  what  is  known 
as  "  bumping"  in  heated  liquids,  and  may  be  largely  mitigated 
by  scraps  of  metal  or  a  dr.op  of  mercury,  or  a  piece  of  charcoal 
weighted  down. 

2.  When  water  has  been  largely  deprived  of  air  and  other  gases 
by  boiling  or  otherwise,  its  boiling  point   is   considerably  raised. 
When  ebullition  commences  there  is  much  more  rapid  generation 
of  steam  than  usual,  with  reduction  of  temperature.     Water  has 
thus  been  heated  from  30°  to  80°  above  its  boiling  point  without 
passing  into  vapor. 

3.  When  salts  are  dissolved  in  liquids,  the  general  effect,  as 
shown  by  Magnus  and  others,  is  to  raise  the  temperature  of  ebulli- 
tion and  also  of  the  vapor  emitted.     Regnault  showed  that  the 
temperature  of  the  vapor  from  such  solutions  soon  falls  to  the 
temperature  of  vapor  disengaged  from  pure  water  under  the  same 
conditions.     From  moderately  pure  water,  for  practical  purposes  it 
may  be  assumed  that  the  vapor  is  at  the  same  temperature  as  though 
the  water  were  pure.     The  steam  emitted  from  saline  solutions  gen- 
erally gives  pure  water,  but  common  salt  is  often  carried  over  from 
salt  water. 

When  a  liquid,  under  given  conditions,  is  vaporized  by  ebulli- 


PRODUCTION  AND   CONDENSATION  OF  VAPOR. 


43 


tion,  the  rapidity  of  vaporization  is  directly  proportional  to  the  heat 
received. 

Applications  Resulting    from  Variations  of  Boiling  Point. — 

From  the  connection  between  the  boiling  point  and  the  pressure 
exerted  upon  the  free  surface  of  the  liquid  result  many  useful  ap- 
plications, among  which  may  be  mentioned — 

The  Measurement  of  Heights  by  the  Boiling  Point  of  Water. — 
Instruments  for  this  purpose  are  called  Ther mo-barometers  or  Hyp- 
someters,  and  consist  of  a  little  boiler  heated  by  a  spirit-lamp  and 
terminating  in  a  tube,  with  an  opening  at  the  side  for  the  escape  of 
the  steam.  A  delicate  thermometer  is  supported  in  the  centre  of 
the  tube,  and  projects  slightly  above  so  as  to  allow  the  temperature 
of  ebullition  to  be  read.  The  thermometer  is  entirely  surrounded 
by  the  steam,  but  does  not  touch  the  liquid.  (See  Fig.  23.)  When 
the  liquid  boils,  the  pressure  of  its  vapor  is 
equal  to  the  atmospheric  pressure.  The 
pressure  of  aqueous  vapor  at  different  tem- 
peratures has  been  determined  and  tabulated. 
By  observing  the  boiling  point  and  refer- 
ring to  the  table,  we  get  the  vapor  pressure 
for  that  temperature,  and  accordingly  the 


J.-THB  HYPSOMKTKR.  FIG.  24.-PApm's  DIOBSTKB. 

pressure  of  the  atmosphere,  from  which  the  height  is  computed. 
An  approximation  is  at  once  obtained  by  using  Soret's  formula, 


44  -  ELEMENTARY  LESSONS  IN  HEAT. 

which  gives  a  decrease  of  1°  C.  in  the  boiling  point  for  each  968 
feet  in  altitude.  The  boiling  point  being  thus  lowered  as  we  go 
upward,  the  dwellers  above  particular  elevations  are  unable  to  per- 
form certain  culinary  operations  in  the  open  air,  and  are  compelled 
to  adopt  means  for  raising  the  boiling  point. 

Papin's  Digester. — The  principle  most  generally  employed  for 
raising  the  boiling  point  is  illustrated  in  Papin's  Digester  (Fig.  24), 
and  is  a  simple  application  of  increase  of  pressure.  The  digester 
is  a  strong  metallic  vessel  in  which  the  water  may  be  heated.  The 
only  opening  to  the  vessel  for  the  escape  of  the  vapor  is  closed  by 
a  valve  pressed  down  by  a  weight.  The  pressure  on  the  valve  can 
thus  be  varied,  and  the  vapor  cannot  escape  until  its  pressure  lifts 
the  valve.  The  pressure  on  the  surface  of  the  liquid  and  the  tem- 
perature of  boiling  may  thus  be  varied  and  regulated. 

It  is  evident  that  this  principle  may  be  applied  equally  at  all 
levels,  and  it  frequently  is,  whenever  it  is  desired  to  heat  water 
above  the  ordinary  boiling  point,  as  in  the  extraction  of  gelatin 
from  bones,  etc.  The  reverse  principle  of  lowering  the  boiling 
point  by  diminishing  the  pressure  is  frequently  made  use  of  to 
evaporate  rapidly  solutions  which  cannot  bear  a  high  temperature, 
by  keeping  them  in  a  space  exhausted  of  air  and  vapor.  An  im- 
portant and  useful  application  of  the  principle  is  made  in  the 
manufacture  of  sugar,  the  liquid  being  slowly  evaporated  in 
vacuum  pans. 

Distillation. — Distillation  is  the  boiling  or  vaporization  of  a 
liquid  and  the  condensation  of  the  vapor  evolved.  It  enables  us 
to  separate  liquids  from  solids  in  solution,  and  to  partially  separate 
liquids  which  rise  in  vapor  at  different  temperatures.  The  appa- 
ratus (Fig.  25)  employed  is  called  a  still,  and  consists  of  a  vessel  a, 
for  heating  the  liquid,  called  a  retort,  and  one  for  condensing  the 
vapor,  called  the  condenser,  and  a  receiver  b.  The  condenser  is 
sometimes  in  the  shape  of  a  spiral  tube,  w,  and  is  then  called  the 
worm  (Fig.  26).  The  condenser  or  worm  is  kept  cool  by  immersion 
in  running  water  or  otherwise,  so  that  the  vapor  is  there  condensed 
and  the  distilled  liquor  collects  in  the  receiver  or  flows  from  the 
worm.  It  is  evident  that,  if  the  air  be  excluded  and  the  vapor 
rapidly  condensed,  the  distillation  will  take  place  at  reduced  tem- 
perature. 


PRODUCTION  AND   CONDENSATION  OF  VAPOR.  45 


FlO.  25.— LlEBIO'S  CONDINSER. 


26.— STILL  WITH  WORM. 


46  ELEMENT  AH  J  LESSONS  IN  HEAT. 

Spheroidal  State. — There  is  a  peculiar  action  of  liquids  when 
dropped  upon  highly-heated  metallic  surfaces  which  may  be  con- 
veniently considered  here,  being  a  case  of  evaporation  though  not 
of  ebullition.  If  water  be  sprinkled  upon  a  highly-heated  metallic 
or  other  smooth  surface,  it  does  not  adhere  to  the  surface,  but 
assumes  an  ellipsoidal  form,  spins  around,  and  moves  about.  The 
liquid  in  this  condition  is  separated  from  the  surface  by  a  cushion 
of  its  own  vapor,  and  its  temperature  is  found  to  be  below  the  boil- 
ing point.  In  this  condition  the  liquid  is  evaporated  less  rapidly 
than  when  the  surface  of  the  metal  is  at  lower  temperature. 

That  the  liquid  remains  below  the  boiling  point  is  due  to  the 
evaporation  which  takes  place  and  to  the  fact  that,  not  being  in 
contact  with  the  plate,  it  is  heated  by  radiation.  The  form  is  the 
consequence  of  cohesion  among  the  molecules  as  modified  by  ex- 
ternal forces,  gravity  and  atmospheric  resistance. 

It  is  possible  that  all  liquids  are  capable  of  assuming  this  state 
but  at  different  temperatures,  dependent  upon  the  liquid  and  the 
nature  of  the  surface.  In  this  state  they  do  not  wet  the  surface  of 
the  plate.  If  the  plate  cools  below  the  particular  temperature  for 
the  liquid,  it  flattens  out  and  evaporates  rapidly  away  with  ebullition. 

We  may  partially  reverse  these  phenomena  by  putting  a  highly 
heated  metallic  ball  into  a  liquid.  For  a  time  the  liquid  will  be 
kept  out  of  contact  with  the  ball  by  a  cushion  of  vapor  produced 
by  the  heat  of  the  ball. 

We  can,  too,  understand  how  the  moist  hand  of  a  man  has  been 
plunged  into  molten  metal  with  impunity;  it  could  not  be  done  in 
a  liquid  at  lower  temperature,  such  as  boiling  water. 

These  phenomena  were  first  examined  by  Leidenfrost  more  than 
a  century  ago,  and  have  since  been  studied  by  other  physicists, 
mainly  Boutigny. 

Freezing  of  Water  and  Mercury  in  a  red-hot  Crucible. — The 
fact  that  a  liquid  assumes  the  spheroidal  state  at  a  temperature 
below  its  boiling  point  enables  us  to  explain  the  seeming  paradox 
of  freezing  water  or  mercury  in  a  hot  crucible.  Thus  Boutigny 
poured  liquid  sulphurous  acid,  whose  boiling  point  is  —10°  0.,  into 
a  white-hot  platinum  crucible.  The  liquid  assumed  the  spheroidal 
state,  and  water  dropped  upon  it  was  immediately  frozen.  Mercury 
has  been  similarly  frozen  by  using  liquid  nitrous  oxide,  whose 
boiling  point  is  —  70°  C.  The  liquids  thus  frozen  do  not  touch 
the  heated  ladle. 


CHAPTER  V. 
CHANGE  OF  STATE. 

Latent  Heat. — It  has  been  mentioned  that  other  effects  than 
change  of  temperature  may  be  produced  by  giving  heat  to  or  taking 
it  from  a  body.  The  heat  which  produces  changes  in  bodies  other 
than  change  of  temperature  is  called  latent  heat. 

Liquefaction. — Latent  Heat  of  Fusion. — Most  solid  bodies  when 
heated  sufficiently  high  change  their  state  from  solid  to  liquid. 
Some  bodies  pass  gradually  from  the  solid  state  through  a  semi- 
solid  state  to  the  liquid  form,  others  pass  abruptly  from  the  solid  to 
the  liquid  state  ;  the  following  remarks  apply  to  the  latter  class. 

This  change  is  called  fusion  or  melting,  and  the  temperature  at 
which  it  takes  place  is  called  the  fusing  or  melting  point,  and  is 
constant  for  the  same  substance  when  the  pressure  is  constant. 
The  temperature  of  the  solid  remains  constant  from  the  time  the 
fusion  commences  until  it  is  finished,  though  heat  must  be  con- 
stantly applied  to  continue  the  melting.  The  heat  thus  transmitted 
to  a  body  without  producing  any  other  effect  that  we  know  of, 
except  a  change  of  state,  is  called  the  latent  heat  of  fusion. 

The  latent  heat  of  fusion  of  a  particular  substance  is  specified 
by  taking  a  unit  weight  of  the  substance,  and  may  be  defined  as  the 
amount  of  heat  expressed  in  thermal  units  necessary  to  melt  or  fuse 
a  unit  weight  of  the  substance  starting  at  the  temperature  of  its 
fusing  point  and  under  atmospheric  pressure. 

If  we  had  a  perfectly  uniform  source  of  heat,  such  that  a  pound 
of  water  at  0°  0.  placed  over  it  would  have  its  temperature  raised 
5°  per  minute,  in  a  little  less  than  sixteen  minutes  the  temperature 
of  the  water  would  be  79°.  The  same  weight  of  ice  at  0°  C.  receiv- 
ing the  same  quantity  of  heat  would  be  converted  into  liquid,  but 
would  not  have  its  temperature  changed.  The  entire  heat  is  con- 
sumed in  changing  the  state  of  the  ice,  but  does  not  affect  its  tem- 

47 


48  ELEMENTARY  LESSONS  IN  HEAT. 

perature,  and  consequently  could  not  be  detected  by  a  thermometer. 
So  far  as  temperature  is  concerned  this  quantity  of  heat  produces 
no  effect,  and  hence  is  called  latent  heat. 

Determination  of  Latent  Heat  of  Fusion. — a.  This  determination 
may  be  made  by  a  method  similar  to  the  "  method  of  mixtures" 
for  specific  heat  determination.  Thus,  if  we  mix  i  pounds  of  ice  at 
0°  0.  with  w  pounds  of  water  at  t°  and  find  the  resulting  tempera 
ture,  as  soon  as  an  equilibrium  is  reached,  to  be  0°,  we  can  find  the 
latent  heat  of  fusion  as  follows  : 

The  units  of  heat  lost  by  the  water  are 

w(t  -  0), 

and  are  spent  partly  in  melting  the  ice  and  partly  in  raising  the 
temperature  of  the  water  produced  from  0°  to  0° ;  then,  if  we 
denote  by  x  the  latent  heat  of  fusion,  we  shall  have 

w(t  -  0)  =  ix  +  iB9 

from  which  x  may  be  found. 

b.  If  any  other  liquid  than  water  be  used,  we  must  know  its 
specific  heat  s,  and  of  any  other  solid  than  ice  we  must  know  its 
fusing  point  T  and  its  specific  heat  s'  in  the  liquid  state  ;  the  above 
formula  will  then  become 

sw(t  —  0)  =  ix  +  is'(0  —  T), 

in  which  the  first  member  is  the  heat  lost  by  the  liquid,  and  the 
second  the  heat  employed  in  melting  the  solid  and  raising  the  tem- 
perature of  the  liquid  produced  from  T°  to  0°.  In  the  above  cases 
the  solid  operated  upon  is  supposed  to  have  been  at  the  tempera- 
ture of  fusion  at  the  beginning  of  the  operation,  but  this  is  not 
necessary  if  we  know  also  the  specific  heat  of  the  solid  body  and 
suppose  it  constant  up  to  the  fusing  point.  If  we  start  with  a 
solid  body  below  the  fusing  point,  say  at  t" 9  and  suppose  s"  to  be 
its  specific  heat,  the  above  equation  will  then  become 

sw(t  -6)=  is"  (T-  /")  +  ix  +  is' (6  -  T), 

in  which  the  first  member  is  the  heat  lost  by  the  liquid  and  spent  in 
raising  the  temperature  of  the  solid  to  fusing  point,  fusing  it,  and 
then  raising  the  temperature  of  the  liquid  from  the  fusing  point 
to0°. 


CHANGE  OF  STATE.  40 

c.  For  substances  which  have  high  melting  points,  a  known 
weight  in  the  molten  state  may  be  enclosed  in  a  small  vessel  and 
immersed  in  the  liquid  ;  then  if  its  initial  temperature,  the  tem- 
perature of  fusion,  and  the  specific  heat  of  the  body  in  the  liquid 
and  in  the  solid  state  be  known,  its  latent  heat  may  be  determined. 

In  all  these  cases  it  is  assumed  that  the  specific  heat  of  the  liquid 
between  the  initial  and  final  temperature  is  constant,  and  the  same 
assumption  is  made  in  regard  to  the  solid  between  the  initial  tem- 
perature and  the  fusing  point.  It  is  also  assumed  that  the  entire 
heat  given  out  by  the  warmer  body  is  transferred  to  the  other,  or 
that  there  is  no  loss  of  heat.  None  of  these  assumptions  is  accu- 
rate, and  the  determinations  are  subject  to  slight  error.  In  c  above 
it  is  also  assumed  that  the  same  amount  of  heat  which  is  absorbed 
in  converting  a  solid  into  a  liquid  is  given  out  when  the  liquid  is 
converted  into  a  solid.  This  can,  however,  be  demonstrated. 

The  fusing  points  and  latent  heats  of  several  substances  are 
given  in  the  accompanying  table  : 


Melting  Point. 

—  39°  C 

Latent  Heat. 
2  82 

0 

79  00 

Tin  o, 

235 

14  20 

332 

5  40 

433 

28  10 

Silver.  . 

.  1000 

21.00 

The  latent  heat  of  ice  is  greater  than  that  of  any  other  substance 
named  in  the  table ;  it  is  14  times  as  great  as  that  of  lead  and  28 
times  that  of  mercury.  Ice  is  more  difficult  to  melt,  and  water 
more  difficult  to  freeze,  than  ti ..y  other  substance, each  being  at  the 
freezing  or  fusing  point.  Those  properties  are  of  great  importance 
in  nature,  retarding  both  freezing  and  thawing. 

Latent  Heat  of  Solution. — The  conversion  of  a  solid  into  a 
liquid  by  solution  is  frequently  accompanied  by  a  disappearance  of 
heat  or  reduction  of  temperature.  This  reduction  of  temperature 
is  consequent  to  the  change  of  state  from  solid  to  liquid.  This  same 
result  is  generally  observed  during  solution  whenever  there  is  no 
chemical  action  between  the  solid  and  liquid.  Thus  the  sweetening 
of  coffee  by  sugar  is  also  a  cooling  process,  and  a  fall  of  from  20° 
to  25°  may  be  obtained  by  dissolving  ammonium  chloride  in  water. 

Solution  takes  place  over  a  wide  range  of  temperatures,  and 
nearly  all  substances  are  more  soluble  at  high  temperatures,  though 


50  ELEMENTARY  LESSONS  IN  HEAT. 

there  are  exceptions.     There  is  accordingly  no  definite  point  of 
solution  corresponding  to  the  point  of  fusion. 

Solidification  or  Congelation.— Solidification  or  congelation 
is  the  process  by  which  a  body  passes  from  the  liquid  to  the  solid 
state, — the  reverse  of  fusion.  In  fusion  heat  becomes  latent  or  pro- 
duces no  effect  on  the  temperature;  in  congelation  the  same  amount 
of  heat  reappears  or  becomes  evident  by  its  effect  on  temperature. 
The  same  number  of  thermal  units  which  have  been  communicated 
to  a  body  without  affecting  its  temperature  in  fusion  will  be  given 
to  the  surrounding  medium  by  the  body  in  solidifying.  In  the  one 
case  addition  of  heat  to  the  body  did  not  affect  its  temperature  ;  in 
the  other  the  temperature  of  the  body  is  not  affected,  although  it 
gives  up  heat  to  the  surrounding  media. 

All  liquids  are  capable  of  being  solidified.  Like  fusion,  with  a 
few  exceptions,  the  change  takes  place  abruptly.  The  temperature 
of  congelation  or  the  freezing  point  is  the  highest  temperature  at 
which  solidification  can  take  place,  and  is  the  same  as  the  fusing 
point  of  the  body  when  solid.  It  is  possible,  however,  to  preserve 
substances  in  the  liquid  state  at  lower  temperatures.  In  case  of 
water  this  result  has  been  accomplished  by  simply  subjecting  to 
cold,  vessels  of  water  perfectly  protected  from  agitation  and  dust. 
Despretz  also  cooled  water  in  narrow  tubes  to  —  20°  C.  without 
freezing.  Dufour  also  obtained  similar  results  by  suspending  water 
in  a  liquid  of  the  same  specific  gravity  and  with  which  it  would 
not  mix. 

A  liquid  thus  reduced  to  a  temperature  below  its  freezing  point 
is  in  general  partially  solidified  by  the  slightest  agitation  or  by  the 
contact  of  any  solid  particles.  Particles  of  its  own  solid  are  sure 
to  produce  the  result. 

When  congelation  commences  under  these  conditions,  it  contin- 
ues until  the  heat  given  out  during  solidification  raises  the  entire 
mass  of  liquid  to  the  freezing  point.  This  may  be  easily  shown  by 
experiment  on  water.  A  small  vessel  containing  water  in  which 
a  thermometer  is  immersed  may  be  cooled  10°  or  12°  below  the 
freezing  point ;  if  freezing  be  then  brought  about  by  a  shock  to  the 
vessel,  the  thermometer  rises  rapidly  to  0°.  Congelation  continues 
until  the  heat  liberated  by  the  water  frozen  raises  the  temperature 
of  the  remaining  liquid  to  0°. 


CHANGE  OF  STATE.  51 

Knowing  the  mass  of  water  involved  and  the  temperature  to 
which  it  is  reduced,  it  is  evident  that  the  quantity  of  ice  that  will 
be  formed  when  congelation  sets  in  may  be  computed. 

The  freezing  of  water  is  sometimes  employed  to  moderate  the 
reduction  of  temperature  in  small  conservatories,  or  other  confined 
spaces. 

Change  of  Volume  in  Solidification. — Most  substances  contract 
in  solidifying,  but  there  are  some  exceptions,  as  water,  bismuth, 
cast-iron,  etc.  This  property  of  bodies  is  very  important,  enabling 
some  of  them  to  be  used  in  castings. 

The  expansion  of  water  in  freezing  is  about  -fa  of  its  volume, 
and  the  enormous  mechanical  force  exerted  thereby  has  already 
been  referred  to.  This  increase  of  volume  also  renders  ice  lighter 
than  water,  and  it  consequently  floats  at  the  surface. 

Effect  of  Pressure  on  the  Freezing  and  Melting  Points.— Sub- 
stances which  expand  in  freezing  have  their  freezing  points 
lowered  by  pressure.  Prof.  J.  W.  Thomson  was  led  to  this  con- 
clusion by  theoretical  considerations,  and  it  has  been  verified  by 
several  experimenters.  It  has  also  been  shown  that  substances 
which  contract  in  freezing  have  their  freezing  points  raised  by 
pressure. 

Mr.  T.  J.  Bottomley  beautifully  illustrated  the  effect  of  pressure 
in  lowering  the  melting  point  of  ice  by  resting  a  block  of  ice  on  two 
supports  a  short  distance  apart,  and  slinging  over  the  ice  a  copper 
wire  to  the  ends  of  which  weights  were  attached.  The  weighted 
wire  gradually  worked  its  way  through  the  ice  and  fell  to  the  floor, 
but  the  block  was  not  cut  in  two, — the  path  made  by  the  wire  was 
filled  by  the  formation  of  new  ice  as  the  wire  advanced. 

Latent  Heat  of  Vaporization. — The  process  of  vaporization  has 
been  already  defined,  and  bodies  which  do  not  volatilize  under 
ordinary  conditions  can  usually  be  made  to  do  so  by  the  application 
of  heat.  Almost  all  bodies  can  be  heated  high  enough  to  convert 
them  into  the  gaseous  state,  if  not  decomposed  before  assuming  this 
state.  Generally  in  assuming  the  gaseous  state  a  solid  passes 
through  the  liquid  state,  though,  as  already  stated,  there  are  some 
which  pass  directly  to  the  gaseous  state. 

A  law  exactly  similar  to  that  accompanying  fusion  universally 


62  ELEMENTARY  LESSONS  IN  SEAT. 

affects  the  gaseous  condition.  The  change  from  a  solid  or  liquid 
state  to  a  gas  is  accompanied  by  the  absorption  of  sensible  heat,  and 
the  reverse  change  by  its  disengagement. 

Many  gases  are  absorbed  or  dissolved  in  large  quantity  by  liquids 
and  thus  are  liquefied,  or  at  least  greatly  condensed,  and  beat  is 
evolved  during  this  condensation  ;  and  during  the  reverse  operation, 
when  the  gas  passes  out  of  the  liquid,  heat  disappears.  All  gases 
have,  however,  been  brought  to  the  liquid  state  proper. 

The  amount  of  heat  which  disappears  in  passing  to  the  gaseouj 
state  varies  with  the  temperature  at  which  the  change  takes  place, 
and  is  exactly  equal  to  that  given  out  when  the  gas  is  condensed  o\ 
returns  to  the  original  form,  provided  both  changes  are  effected  a( 
the  same  temperature.  The  heat  absorbed  by  a  liquid  during  con 
version  into  vapor  or  gas  is  called  the  latent  heat  of  vaporization. 

The  amount  of  heat  necessary  to  convert  a  pound  of  water  v , 
100°  C.  into  steam  at  100°  is  537  units  ;  that  is  to  say,  the  hea? 
necessary  to  evaporate  one  pound  of  water  at  100°  is  sufficient  to 
raise  537  pounds  of  water  one  degree  in  temperature.  This  same 
amount  of  heat  reappears  in  the  condensation  of  the  pound  of 
steam  at  100°;  that  is  to  say,  a  pound  of  steam  at  100°  by  its 
condensation  to  water  would  raise  5.37  pounds  of  water  from  0°  to 
100°  C.  The  latent  heat  of  steam  at  100°  C.  is  537.  The  latent 
heat  of  the  vapor  of  water  decreases  as  the  temperature  rises. 
Vapors  of  other  liquids  have  less  latent  heat  .than  steam.  The 
accompanying  table  gives  the  latent  heats  of  the  vapors  named  at 
the  boiling  points  of  their  respective  liquids  under  atmospheric 
pressure.  The  third  column  gives  the  approximate  volumes  of 
vapor,  under  atmospheric  pressure,  given  off  from  one  volume  of 
each  of  the  liquids  at  their  boiling  points. 

Boiling  Point.    Latent  Heat.  Volume  of  Vapor  from 

C.  C.  one  Volume  Liquid. 

Water 100°  537  1696 

Alcohol 78°  202  528 

Carbon  bisulphide 46°                    87  420 

Ether 35.5°               90.5  298 

Ammonia* -38.5°  259  850f 

*  Principles  of  Chemistry,  vol.  i.  p.  246,  Mendeleef. 

f  These  numbers,  taken  in  connection  with  the  specific  gravities  and  specific 
heats  of  the  liquids,  and  the  ready  solubility  of  ammonia  in  water,  have  sug- 
gested the  possibility  of  using  it  in  competition  with  steam  for  driving  engines. 
If  equal  weights  of  ammonia  and  water  be  converted  into  vapor  at  100°,  the 
volume  of  the  ammonia  vapor  is  slightly  greater  than  that  from  water. 


CHANGE  OF  STATE.  53 

Latent  Heat  of  Aqueous  Vapor. — We  have  stated  above  that  the 
heat  given  out  in  the  condensation  of  a  vapor  is  equal  in  amount  to 
that  absorbed  in  its  vaporization,  provided  both  changes  take  place 
at  the  same  temperature.  If  they"  do  not  take  place  at  the  same 
temperature,  these  amounts  are  not  equal. 

The  results  of  Kegnault's  labors  in  connection  with  the  sub- 
ject of  latent  heat  have  established  the  following  facts  in  regard  to 
aqueous  vapor : 

The  quantity  of  heat  required  to  convert  a  pound  of  water  at 
100°  C.  into  vapor  at  the  same  temperature  is  537  thermal  units. 
If  we  start  with  the  water  at  0°  C.,  raise  it  to  100°  C.,  then  vapor- 
ize it  without  change  of  temperature,  the  total  will  be  637  thermal 
units.  It  is  this  total  amount  which  it  is  most  important  to  know 
in  the  applications  of  heat  in  the  arts. 

In  general,  if  we  denote  by  Q  the  total  amount  of  heat  required 
to  raise  the  temperature  of  a  unit  weight  of  water  from  0°  to  T3, 
and  vaporize  it  at  that  temperature,  the  value  of  Q  is  given 'by  the 
formula : 

Q  =  606.5  +  0.305  T.     (a) 

From  what  is  said  above  we  see  that,  if  we  denote  by  A,  the 
latent  heat  of  vaporization  at  T,  we  will  have 

Q  =  *  +  T, 
and  by  substituting  this  value  of  Q  in  (a)  we  have 

\  =  606.5  -0.69577, 

from  which  it  appears  that  the  latent  heat  of  water  decreases  as 
the  temperature  rises. 

By  considering  the  slight  variation  of  the  specific  heat  of  water 
with  change  of  temperature,  Regnault  found  the  latent  heat  of 
vapor  of  water  to  be  at  0°  C.  606.5,  at  100°  C.  536.5,  and  at  200°  C. 
464.3.  Watt  was  aware  of  the  decrease  of  the  latent  heat  of  steam 
with  increase  of  temperature,  but  he  thought  that  the  sum  of  the 
two  remained  constant.  The  above  numbers  added  in  indicated 
pairs  show  that  there  is  considerable  error  in  Watt's  idea. 

Latent  Heat  of  Expansion. — When  a  gas  expands,  heat  must  be 
communicated  to  it  in  order  to  keep  its  temperature  the  same:  this 
may  be  called  the  latent  heat  of  expansion.  If  the  gas  be  com- 
pressed by  external  force,  its  temperature  will  be  increased. 

In  all  these  cases  in  which  heat  is  said  to  become  latent  it  must 


54  ELEMENTARY  LESSONS  IN  HEAT. 

be  kept  in  mind  that  there  is  no  loss  of  heat  energy.  Heat  when 
applied  to  bodies  produces  several  effects,  one  of  which  is  usually  a 
change  of  temperature  ;  if  it  produces  other  effects  and  no  change 
of  temperature,,  it  is  called  latent.  These  other  effects  above  given 
are  fusing  solids,  vaporizing  liquids,  expanding  gases.  The  heat 
applied  has  altered  the  relations  of  the  particles  of  the  body, 
probably  by  changing  their  positions ;  and,  when  these  particles 
assume  their  original  relations,  that  other  effect  of  heat,  temper- 
ature, is  observed. 

Utilization  of  Latent  Heat. — There  are  many  practical  applica- 
tions which  depend  upon  the  foregoing  laws  involved  in  the  change 
of  state  of  bodies.  The  thermic  effects  accompanying  the  changes 
of  state  of  water  are  also  very  important. 

Freezing- Mixtures. — Common  freezing-mixtures  are  efficient  be- 
cause of  the  heat  absorbed  in  the  liquefaction  of  solids.  In  all  such 
mixtures  there  is  at  least  one  solid  substance  which  is  reduced  to 
the  liquid  state  by  the  action  of  the  others,  thus  producing  a  fall  of 
temperature  proportional  to  the  latent  heat  of  fusion  of  the  sub- 
stance. When  two  solids  or  a  liquid  and  solid  are  brought  together 
and  produce  a  mixture  which  is  liquid,  cold  will  be  produced  unless 
there  be  strong  chemical  action  between  the  bodies.  ODC  of  the 
most  common  of  such  mixtures  is  that  of  snow  and  salt,  in  which 
both  the  snow  and  the  salt  are  brought  to  the  liquid  state  with  a 
reduction  of  temperature  to  0°  F.  Powdered  crystallized  calcium 
chloride  and  snow  will  produce  a  much  greater  cold  (—40°  C.). 
The  mere  solution  of  bodies  in  water,  when  unaccompanied  by 
energetic  chemical  action,  will  produce  marked  fall  of  temperature. 
Thus  the  solution  of  nitre  or  ammonium  chloride  or  ammonium 
nitrate  in  water  at  ordinary  temperature  will  produce  a  fall  of  from 
15°  to  25°  C. 

Cold  by  Evaporation. — The  latent  heat  of  evaporation  can  in 
many  ways  be  taken  advantage  of  to  produce  cold.  Those  liquids 
which  evaporate  most  rapidly  produce  the  greatest  reduction  of 
temperature.  If  the  hand  be  moistened  with  alcohol  or  ether,  a 
decided  sensation  of  cold  is  experienced  ;  with  water  the  effect  is 
less  marked,  because  it  evaporates  more  slowly. 

Leslie's  experiment  consisted  in  showing  that  water  could  be 
frozen  by  the  cold  resulting  from  its  own  evaporation.  A  thin 


CHANGE  OF  STATE. 


FIG.  27.— LESLIE'S  EXPERIMENT. 


metallic  vessel  (Fig.  27)  containing  a  little  water  was  placed  over  a 
vessel  containing  strong  sulphuric  acid,  the  whole  being  placed 
under  the  receiver  of  an  air-pump.  As  the  air  is  exhausted  the 
water  evaporates  more  and  more  rapidly,  the  vapor  of  water  being 
absorbed  by  the  sulphuric 
acid,  and  ice  soon  forms  on 
the  surface.  To  make  this 
experiment  a  success  it  is 
necessary  to  remove  the 
vapor  of  water  as  fast  as  it 
is  formed,  which  is  diffi-  _ 
cult  to  do  with  the  arrange- 
ment given,  for  the  absorb- 
ing power  of  the  sulphuric 
acid  diminishes  as  the  surface  layer  becomes  diluted  by  the  vapor 
first  escaping,  and  the  vapor  more  remote  from  the  acid  is  only  im- 
perfectly absorbed.  Air-pumps  are  now  constructed  which  at  each 
stroke  force  the  vapor  drawn  from  the  water  into  reservoirs  of 
sulphuric  acid,  and  insure  the  success  of  the  experiment. 

Wollaston's  Cryopliorus. — This  instrument  is  sometimes  used  to 
show  the  freezing  of  water  by  its  own  evaporation.  It  consists  of  a 
U-shaped  tube  (Fig.  28)  with  a  bulb  at  each 
end,  and  is  partly  filled  with  water,  the  air 
having  been  'expelled  by  hermetically  sealing 
the  tube  while  the  liquid  was  in  a  state  of 
ebullition.  When  an  experiment  is  to  be  made, 
all  the  liquid  is  passed  into  one  bulb  and  the 
other  is  plunged  into  a  freezing-mixture.  Th$. 
cold  condenses  the  vapor  from  the  water  and 
thus  facilitates  evaporation  until  ice  appears  on. 
the  surface  of  the  liquid. 

When  other  liquids  more  volatile  than  watej 
are  employed  much  more  intense  cold  can  bt 
produced.  Water  contained  in  a  thin  tube 
dipped  into  a  glass  containing  ether  may  be 
frozen  by  causing  the  ether  to  evaporate  rapidlv 

FIG.  28.-WQLLASTON1S  J  .-.*..,  ,       .        -  *        ? 

CRYOPHORUS.  by  agitating  it  with  a  current  of  air  from  a  pai? 

of  hand-bellows.    Mercury  may  be  frozen  by  liquid  sulphurous  acici, 
which  is  much  more  volatile  than  ether. 


56  ELEMENTARY  LESSONS  IN  HEAT. 

Ice-Machines. — Most  machines  for  the  artificial  preparation  of 
ice  depend  for  their  action  upon  the  cold  produced  by  evaporation. 
In  Carres  machine  the  evaporation  takes  place  from  liquid  am- 
monia, the  vessel  of  water  to  be  frozen  being  surrounded  by  the 
ammonia.  The  vapor  of  the  evaporating  ammonia  p^ses  into  a 
second  vessel  containing  water,  by  which  it  is  greedily  absorbed  and 
thus  removed  from  over  the  evaporating  liquid.  By  applying  heat 
to  the  second  vessel  the  ammonia  may  be  again  driven  out  of  the 
water  and  condensed  in  the  liquid  state  in  the  first,  and  the  opera- 
tion repeated. 

In  many  other  machines  in  this  country  the  evaporating  liquids, 
which  are  usually  ammonia  or  some  of  the  more  volatile  petroleum 
compounds,  are  condensed  by  pressure  and  cold  and  then  allowed 
to  evaporate  through  a  series  of  pipes  immersed  in  a  strong  solution 
of  salt.  The  salt  solution  is  thus  cooled  to  such  a  degree  that  ves- 
sels of  water  placed  in  it  are  quickly  frozen.  The  vapor  of  the 
evaporating  liquid  as  it  passes  into  the  pipes  is  continually  pumped 
out  and  returned  to  the  condenser  in  a  liquid  state. 

Liquid  carbonic  acid,  when  permitted  to  escape  from  a  vessel 
through  a  narrow  orifice,  evaporates  so  rapidly  that  a  portion  of  the 
vapor  freezes  and  falls  as  snow.  Faraday,  with  this  carbonic-acid 
snow  dissolved  in  ether  and  placed  under  the  receiver  of  an  air-pump, 
obtained  a  temperature  of  —  166°  F. 

Alcohol  has  been  solidified  by  Wroblewski  and  Olszewski  by 
adopting  the  method,  first  suggested  by  Cailletet,  of  using  liquefied 
ethylene  as  the  means  of  producing  cold.  The  boiling  point  of  this 
substance  under  atmospheric  pressure  is  between  —102°  and  —103° 
C.,  and  the  temperature  produced  by  boiling  it  in  vacua  is  lower  the 
more  perfect  the  vacuum.  The  above-named  experimenters  obtained 
a  temperature  of  —136°  C.  by  means  of  it.  They  determined  that 
carbon  bisulphide  solidified  at  —116°  C.,  and  alcohol  became  viscous 
at  about  —129°  C.  and  solidified  to  a  white  mass  at  —130.5°  C. 
The  critical  temperature  of  oxygen  is  lower  than  the  boiling  point 
of  ethylene  in  air,  and  it  commenced  to  liquefy  at  —131.6°  under 
26.5  atmospheres.* 

Heating  by  Steam. — The  large  amount  of  heat  given  out  by 
steam  in  condensing,  and  its  rapid  circulation  even  under  slight 
pressure,  have  led  to  its  use  as  a  means  of  heating. 

*  Comptes  Rendus,  April  16,  1883. 


CHANGE  OF  STATE.  57 

The  steam  is  generated  in  boilers  and  conducted  by  iron  pipes 
to  the  building  to  be  heated.  The  circulating  pipes  should  be  so 
arranged  as  to  secure  an  expeditious  return  of  the  water  from  the 
condensed  steam  to  a  receptacle  from  which  it  may  be  again  forced 
into  the  boiler.  This  may  be  accomplished  by  giving  the  pipes  an 
inclination  in  the  proper  direction. 

Irregularities  in  the  fires  under  the  boilers  affect  very  quickly 
the  circulation  of  steam.  When  the  fires  are  too  low  the  steam 
condenses  along  the  pipes,  circulation  largely  ceases,  and  a  partial 
vacuum  exists.  When  the  fires  become  hot  again  the  steam  rushes 
into  the  pipes  of  the  ordinary  construction  and,  meeting  the  water, 
hurls  it  forward  violently,  producing  very  disagreeable  noises  and 
sometimes  cracks  in  the  pipes.  These  disagreeable  noises,  and  the 
fact  that  the  steam-heaters  do  not  of  necessity  enforce  ventilation, 
are  the  main  objections  to  this  method  of  heating. 


CHAPTER  VI 
HYGROMETRY. 

Eygrometry  in  its  broadest  sense  is  that  branch  of  science  which 
has  for  its  object  the  measurement  of  the  humidity  of  substances. 
Hygrometry,  however,  is  generally  restricted  to  the  measurement 
of  the  amount  of  aqueous  vapor  in  the  air,  on  account  of  the  para- 
mount importance  of  this  branch  of  the  subject. 

Absolute  Humidity.  —  The  condition  of  the  air  as  regards 
moisture  depends  both  upon  the  temperature  of  the  air  and  the 
amount  of  aqueous  vapor  present. 

The  actual  amount  of  vapor  present  in  a  given  amount  of  air  is 
expressed  by  the  term  absolute  humidity.  This  amount  may  in- 
crease or  decrease  considerably  with  the  temperature  without  affect- 
ing our  sensations  of  dryness  or  moisture. 

Relative  Humidity. — Our  sensations  of  moisture  and  dryness, 
and  the  terms  humid  and  moist  in  ordinary  language,  nearly  corre- 
spond to  the  meteorological  term  relative  humidity,  and  depend  upon 
the  condition  of  the  air  as  regards  saturation.  In  warm  weather 
the  air  is  generally  drier  than  in  cold,  though  the  actual  amount  of 
vapor  present  is  greater.  This  is  because  the  capacity  of  air  for  vapor 
is  greater  at  higher  temperature. 

Since  a  cubic  foot  of  air  will  contain  as  much  vapor  as  a  cubic 
foot  of  space  without  air,  we  may  define  relative  humidity  as  the 
ratio  of  the  mass  of  vapor  present  in  a  space  to  the  mass  ivhich  would 
saturate  the  space  at  the  actual  temperature. 

Since  aqueous  vapor  follows  approximately  Boyle's  law,  the 
pressures  will  be  directly  as  the  densities,  and  we  may  also  define 
the  relative  humidity  as  the  ratio  of  the  actual  vapor  pressure  to 
the  maximum  vapor  pressure  for  the  temperature. 

58 


HYGROMETRY. 


59 


If  the  absolute  humidity  remain  constant,  the  relative  humidity 
will  vary  in  the  opposite  direction  to  the  temperature  until  satura- 
tion is  reached,  and  the  dryness  and  moisture  of  the  atmosphere 
will,  in  the  main,  vary  in  the  same  way.  Relative  humidity  is 
usually  expressed  as  a  percentage. 

Dew-Point. — In  general  the  atmosphere  is  not  saturated  with 
vapor,  and  if  it  be  continually  cooled  the  density  of  the  vapor  will 
increase  until  it  reaches  a  maximum,  and  any  further  reduction  of 
temperature  will  cause  a  portion  of  the  vapor  to  liquefy.  The 
temperature  at  which  saturation  is  reached  is  called  the  dew-point. 

Hygroscopes  -  These  instruments  give  simply  indications  as 
to  the  relative  humidity  or  dryness  of  the  air.  Their  construction 
depends  upon  a  property,  common  to  nearly  all  organic  substances, 
of  changing  their  dimensions  by  absorb- 
ing moisture  as  the  air  becomes  damp 
and  giving  it  off  when  dry.  During 
these  changes  variations  of  volume  occur, 
which  may  be  used  to  indicate  the  hygro- 
metric  condition  of  the  air.  The  result 
of  absorption  of  moisture  is  generally  in- 
crease of  volume,  and,  if  the  body  be 
composed  of  twisted  fibres  as  are  ropes 
and  cords,  the  increase  of  length  may 
not  be  sufficient  to  counterbalance  the 
increase  in  cross-section  of  the  fibres, 
and  such  bodies  grow  shorter  when  wet. 

Saussure's  Hygrometer. — This  is  but 
a  hygroscope  in  which  a  hair,  deprived 
of  grease,  is  made  to  move  a  needle 
by  its  contraction,  and  when  the  hair 
expands  the  needle  is  moved  in  the 
opposite  direction  by  a  weight.  The 
weight  keeps  the  hair  always  taut.  Ex- 
cept in  the  very  cold  climates  of  Russia 
and  Siberia  this  instrument  is  simply  a  FIG.  SO.- 

hygroscope,  but  there  it  is  used  as  an  in..  HYGROMETER. 

strument  of  observation,  because  of  the  difficulty  of  making  obser- 


60 


ELEMENTARY  LESSONS  IN  HEAT. 


vations  at  such  low  temperatures  with   the   hygrometer  proper. 
One  form  of  the  instrument  is  shown  in  Fig.  29. 

To  the  class  of  hygroscopes  belong  many  of  the  chimney  orna- 
ments in  popular  use  for  "weather  indicators."  One  of  the  most 
common  forms  is  that  in  which  the  figure  of  a  man  or  woman  is 
made  to  step  out  from  a  toy  house,  depending  on  the  dampness  or 
dryness  of  the  air.  Another  form  is  that  in  which  a  monk  is  made 
to  draw  a  cowl  over  his  head  when  the  air  is  damp.  Certain 
chemical  substances  will  change  color  by  loss  and  gain  of  moisture, 
and  they  can  be  used  to  give  indications  of  the  moisture  present 
in  the  air. 

Hygrometers. — Instruments  intended  to  furnish  accurate  in- 
formation as  to  the  state  of  the  air  in  regard  to  moisture  are  called 
hygrometers. 

They  may  be  divided  into  three  classes  : 

1st.  Hygrometers  of  condensation,  or  dew-point  hygrometers. 

2d.  Hygrometers  of  evaporation,  or  wet  and  dry  bulb  hygrome- 
ters, also  called  psych rometers. 

3d.  Chemical  hygrometers,  which  directly  measure  the  weight 
of  vapor  in  a  given  volume  of  air. 

Dew-Point  Hygrometers. — The  principle  of  this  class  is  illus- 
trated when  a  body  cools  in  a  moist  atmosphere,  as  when  a  glass 
of  water  in  damp  air  is  cooled  by  dropping  in  fragments  of  ice.  As 
the  vessel  is  cooled  the  layer  of  air  in  contact  with  it  is  also  cooled, 
and  finally  moisture  makes  its  a  ppearance  on  the  outside  of  the 
vessel,  and  the  temperature  at  which  this  occurs  is  the  dew-point, 
which  may  be  known  from  a  delicate  thermometer  immersed  in 
the  vessel. 

Dines 's  Hygrometer  is  a  good  one  of  this  class,  and  consists  of 


Fia.  30.— DINES'S  HYGROMETER  (SECTION). 

a  small  flat  chamber  covered  with  thin  black  glass.  (Fig.  30).     This 
chamber  contains  a  delicate  thermometer,  and  is  connected  by  a 


HYGROMETRY. 


61 


pipe  with  a  reservoir  of  water,  which  is  gradually  cooled  b}r  drop- 
ping in  ice.  The  chamber  also  has  a  discharge-pipe  through  which 
the  water  flows  when  the  chamber  is  full.  The  water  is  admitted 
to  the  chamber  by  turning  a  stopcock,  and,  after  filling,  the 
chamber  overflows  through  the  waste-pipe.  As  soon  as  the  dew 
is  seen  on  the  black  glass,  the  thermometer  is  read  and  the  stop- 
cock turned  off.  When  the  moisture  disappears  the  thermometer 
is  read  again,  and  the  mean  of  the.  readings  gives  the  dew-point. 

Daniell's  Hygrometer. — This  instrument  consists  of  a  bent  glass 
tube  with  a  bulb  at  each  end.  (Fig.  31.)  It  contains  only  ether  and 
the  vapor  of  ether,  the  air  having  been  expelled  in  tha  making  of 
the  tube.  One  of  the  bulbs,  A,  is  made  of  blackened  glass,  and  that 
limb  of  the  tube  also  contains  an 
enclosed  thermometer.  To  use 
the  instrument  the  whole  of  the 
ether  is  passed  into  the  bulb  A, 
and  the  other  bulb,  which  is  sur- 
rounded by  muslin,  is  moist- 
ened externally  with  ether.  The 
evaporation  of  this  ether  from 
the  muslin  causes  a  condensation 
of  the  vapor  of  ether  on  the  in- 
side of  this  bulb,  with  a  diminu- 
tion of  pressure.  This  difference 
of  pressure  produces  a  transfer 
of  vapor  from  A  to  B,  with  re- 
newed evaporation  from  the  sur- 
face of  the  ether  in  A,  and  a 
reduction  of  temperature  in  this 
part  of  the  instrument.  The  mo- 
ment the  dew  appears  On  the  FIG.  31.— DANIELL'S  HYGROMETER. 
blackened  surface  of  the  bulb,  the  temperature  of  the  enclosed 
thermometer  is  read.  If  the  temperature  is  again  read  at  the 
moment  of  disappearance  of  the  dew,  the  mean  of  the  two  readings 
will  give  the  dew-point  more  accurately  than  either  separately. 

The  temperature  of  the  air  is  given  by  a  thermometer  attached 
to  the  stand  of  the  instrument. 

RegnauU's  Hygrometer. — This  instrument  (Fig.  32)  consists  of 
two  glass  tubes,  A  and  B,  terminating  at  the  bottom  in  polished 


ELEMENTARY  LESSONS  IN  HEAT. 


silver  cups  which  are  nearly  filled  with  ether.  A  thermometer 
passes  through  the  stopper  of  each  tube  and  has  its  bulb  dipping 
into  the  ether.  The  tube  B  has  also  two  smaller  glass  tubes,  c  and 
d,  passing  through  its  stopper.  The  lower  end  of  the  tube  c  dips 
well  into  the  ether,  and  the  upper  end  is  open  to  the  external  air. 
The  tube  d  passes  through  the  stopper  but  does  not  extend  to  the 
ether.  The  outer  end  of  this  tube  is  connected  by  a  rubber  tube 

to  a  cylindiical  vessel,  F,  which 
is  closed  at  one  end  by  a  stop- 
cock. This  vessel  when  filled 
with  water  constitutes  the  as- 
pirator. To  make  an  observa- 
tion with  this  instrument,  both 
stopcocks  are  opened,  and,  by 
the  escape  of  the  water  from 
the  aspirator,  air  is  drawn  from 
the  tube  B,  and  the  external  air 
passes  through  the  tube  c  to 
supply  its  place.  This  inflowing 
air  produces  agitation  in  the 
ether,  causing  evaporation  and 

FIG.  32.— REGNAULT'S  HYGROMETER.  consequent  reduction  of  temper- 
ature, and  at  the  same  time  tends  to  preserve  a  uniform  temper- 
ature throughout  the  ether. 

When  the  temperature  of  the  ether  has  been  thus  sufficiently 
lowered,  a  deposit  of  dew  will  take  place  upon  the  silver  surface, 
which  is  more  readily  seen  by  contrast  with  the  other  cup.  The 
reading  of  the  enclosed  thermometer  at  the  first  appearance  of  the 
dew  on  the  silver  gives  the  dew-point.  The  mean  of  its  readings 
at  the  appearance  and  disappearance  of  the  dew  is  usually  taken  as 
the  correct  temperature.  The  thermometer  in  the  other  tube  in- 
dicates the  temperature  of  the  air.  Neither  in  this  instrument  nor 
in  DanielPs  can  the  indications  be  too  high  if  the  thermometers  are 
accurate  and  the  readings  correct,  but  they  may  be  too  low. 

Alcohol  may  be  used  in  this  instrument  instead  of  ether,  which 
is  an  important  advantage,  since  the  boiling  point  of  ether  is  so 
low  (36°  C.)  that  it  is  difficult  to  preserve  it  in  hot  climates.  The 
agitation  of  the  liquid  and  the  fact  that  it  is  contained  in  a  silver 


HYGROMETRT.  63 

or  good  conducting  holder  are  both  important  advantages  over 
Darnell's  hygrometer. 

When  the  dew-point  is  known,  the  humidity  may  be  deter- 
mined, as  will  appear  from  the  following  considerations: 

If  a  mixture  of  air  and  vapor  be  subjected  to  changes  of  temper- 
ature, pressure,  or  volume,  and  none  of  the  vapor  be  condensed, 
both  constituents  will  be  affected  alike,  since  they  both  obey  Boyle's 
law  and  have  the  same  coefficient  of  expansion.  In  such  a  mix- 
ture, if  a  change  of  volume  and  temperature  occur  at  the  same 
time  as  in  cooling,  the  pressure  of  each  constituent  and  the  total 
pressure  will  all  be  increased  or  decreased  alike.  In  other  words, 
the  pressure  of  each  constituent  and  the  total  pressure  will  each  be 
multiplied  by  the  same  factor.  Now,  if  the  total  pressure  remains 
the  same  during  a  change  of  volume  and  temperature  of  such  a 
mixture,  the  constituent  pressures  will  also  remain  unchanged. 
The  total  pressure  does  remain  the  same  (that  of  the  atmosphere) 
when  there  is  free  communication  between  the  altered  air  and  the 
general  atmosphere;  consequently  the  constituent  pressures  are 
the  same. 

It  therefore  follows  that  cooling  the  air  down  to  the  dew-point 
does  not  alter  the  vapor  pressure.  The  actual  vapor  pressure  in 
any  portion  of  air  is,  therefore,  equal  to  its  maximum  pressure  at 
the  dew-point. 

The  dew-point  might  also,  therefore,  be  defined  as  the  tempera- 
ture at  which  vapor  at  its  maximum  density  would  have  the  same 
pressure  as  that  in  the  air  at  the  time. 

If  we  know  the  dew-point,  we  can  find  at  once  from  tables  of 
vapor  pressure  the  pressure  of  the  vapor  in  the  air ;  and  if  we  have 
the  temperature  of  the  air,  we  can  find  from  the  same  tables  what 
the  pressure  would  be  at  saturation  for  that  temperature.  The 
ratio  of  the  former  to  the  latter  is  the  relative  humidity. 

Under  the  assumption  that  aqueous  vapor  has  the  same  coeffi- 
cient of  expansion  as  air,  and  equally  obeys  Boyle's  law,  it  follows 
that  the  ratio  of  the  density  of  aqueous  vapor  to  that  of  the  air  at 
different  temperatures  and  pressures  is  constant.  This  ratio,  as 
determined  by  Gay-Lussac,  Regnault,  and  others,  may  be  taken  as 
.623,  and  it  may  be  considered  as  constant  within  the  ordinary 
range  of  temperature  and  pressure  which  exist  in  the  atmosphere. 


64 


ELEMENTARY  LESSORS  IN  HEAT. 


Aqueous  vapor  is  therefore  .623  ($  nearly)  as  heavy  as  air  at  the 
same  pressure  and  temperature.  This  same  fraction  (to  within 
ToVfr)  for  the  density  of  aqueous  vapor,  referred  to  air  at  the  same 
pressure  and  temperature,  is  given  by  the  law  of  volumes.  The 
above  relations  give  the  means  for  the  determination  of  the  absolute 
humidity  or  actual  amount  of  vapor  in  the  air;  for  the  weight  of 
the  unit  of  volume  of  air  at  the  standard  pressure  and  temperature 
has  been  very  accurately  determined.  This  weight,  as  adopted  by 
the  International  Bureau  of  Weights  and  Measures,  for  a  cubic  foot 
of  air  at  32°  F.  and  under  30  inches  pressure  is  566.53  grains. 
From  the  constants  above  given,  the  weights  in  the  table  on  page 
35  are  computed.  The  tables  of  vapor  pressure  adopted  by  meteo- 
rologists are  those  made  by  Regnault. 

Hygrometers  of  Evaporation. — TJie  Psychrometer,  or  Wet  and 
Dry  Bulb  Hygrometer. — This  instrument  consists  of  two  precisely 
similar  thermometers  mounted  at  a  short 
distance  from  each  other.  The  bulb  of  one 
is  covered  with  muslin  and  kept  moist  by  ca- 
pillary action  through  a  string  leading  from  a 
vessel  of  water.  (See  Fig.  33.)  The  vessel 
should  have  only  a  small  surface  of  liquid 
exposed,  should  be  placed  some  distance 
from  the  thermometer,  and  should  be  at 
such  level  as  to  keep  the  muslin  well  moist 
but  not  dripping  wet. 

When  the  temperature  of  the  air  is  below 
freezing,  the  covered  bulb  must  be  dipped 
into  the  water  and  removed,  and  the  water 
adhering  to  the  bulb  allowed  to  freeze.  The 
evaporation  then  takes  place  from  the  shell 
of  ice. 

The  observations  in  both  cases  consist 
simply  in  noting  the  reading  of  the  ther- 
mometers. 

The  difference  of  reading  between  the 
two  thermometers  will  evidently  be  greatest 
when  the  air  is  driest.  The  facility  of  observation  with  this 


\ 


Fio.  33. 

THK  PSYCHROMKTEB. 


HYGBOMETRY. 


65 


instrument  at  ordinary  temperatures,  and  in  extremely  dry  regions 
where  the  hygrometers  of  condensation  act  with  difficulty,  has 
brought  it  into  very  general  use. 

For  meteorological  observations  in  the  field,  as  distinguished 
from  observations  at  permanent  stations,  and  for  hygrometric 
observations  in  connection  with  barometric  hypsometry  in  the 
various  surveys  conducted  in  this  country,  the  psychrometer  is 
indispensable. 

Empirical  tables  have  been  constructed  by  a  comparison 
of  the  simultaneous  readings  of  the  psychrometer  and  DauielPs 


FIG.  34.— CHEMICAL  HYGROMETER. 

hygrometer,  taken  at  Greenwich  and  other  places  for  a  series  of 
years.  These  tables  give  a  ready  means  for  determining  the  dew- 
point  from  the  observations  of  the  psychrometer.* 

For  many  years  it  has  been  attempted  to  construct  a  rational 
formula  for  determining  the  dew-point  from  the  observations  of 
the  psychrometer,  but  it  has  been  very  difficult  to  eliminate  uncer- 
tain assumptions  from  the  data  necessary  to  the  solution  of  the  prob- 
lem. Some  of  the  recent  formulae  are  however  satisfactory. 

Chemical  Hygrometer. — This  apparatus  (Fig.  34)  consists  sim- 
ply of  an  aspirator  filled  with  water  and  connected  at  its  upper 

*  See  note,  p.  166,  Appendix. 


66  ELEMENTARY  LESSONS  IN  HEAT. 

extremity  with  a  series  of  U -tubes  containing  pumice  soaked  in 
sulphuric  acid.  The  water  is  allowed  to  flow  out  of  the  aspirator 
by  the  lower  stopcock ;  the  air  which  enters  the  aspirator  to  re- 
place the  water  is  obliged  to  pass  through  the  tubes  and  leaves  the 
moisture  in  them.  The  moisture  from  the  air  is  left  in  the  first 
tubes;  the  last  tube  is  to  absorb  any  moisture  which  might  pass 
backward  from  the  aspirator.  The  increase  of  weight  in  the  tubes 
evidently  gives  the  weight  of  moisture  which  was  in  the  air  ad- 
mitted, the  volume  of  which  is  known  by  the  volume  of  water 
which  has  escaped. 


CHAPTER  VII. 
CONDUCTION. 

any  portion  of  a  metallic  body  is  subjected  to  a  higher 
temperature  than  other  portions,  there  is  at  first  a  gradual  rise  of 
temperature  in  the  surrounding  parts,  which  is  more  rapid  near  the 
source  of  heat.  After  a  time  the  temperatures  of  the  different 
parts  of  the  body  cease  to  rise,  and  remain  constant  so  long  as  the 
source  of  heat  and  other  conditions  are  unchanged. 

These  effects  can  only  occur  by  the  transference  of  heat  from 
part  to  part  of  the  body  through  the  intermediate  parts.  This 
transfer  of  heat  through  contiguous  matter,  leaving  always  parti- 
cles nearer  the  source  at  higher  temperatures  than  others  more 
distant,  is  called  conduction,  but  there  are  two  stages  in  the 
process. 

1.  Variable  Stage— Diffusivity. — When  any  part  of  the  body  as 
above  stated  is  first  subjected  to  a  higher  temperature,  there  is  a 
gradual  and  continuous  rise  of  temperature  in  all  the  adjoining 
portions.  This  variable  stage  is  known  by  changes  of  temperature 
in  the  body,  and  therefore  depends  not  only  upon  the  heat  trans- 
mitted from  portion  to  portion  of  the  metal,  but  also  upon  its 
specific  heat.  In  this  case  it  is  evident  that,  since  the  temperature 
of  each  portion  of  the  metal  rises,  a  part  of  the  heat  transmitted  to 
any  particle  is  not  passed  onward  but  remains  in  the  particle,  as  is 
evidenced  by  the  increase  of  temperature.  This  transfer  of  heat, 
with  accompanying  partial  consumption  in  elevating  the  tempera- 
ture of  the  medium  of  transfer,  measures  the  diffusivity  or  ther- 
mometric  conductivity.  It  varies  directly  with  the  transferring 
power  of  the  metal,  and  inversely  as  the  specific  heat  per  unit  of 
volume. 

67 


68  ELEMENTARY  LESSONS  IN  HEAT. 

2.  Permanent  Stage  of  Conduction.— The  source  of  heat  and 
other  conditions  remaining  constant  in  the  case  supposed,  the 
temperatures  of  all  parts  of  the  body  after  a  time  cease  to  change 
and  remain  constant.  By  air-contact  and  radiation  all  the  surface 
particles  of  the  warm  metal  are  still  giving  off  heat,  and  since 
their  temperatures  do  not  fall,  heat  is  still  being  transferred  to 
them  from  the  source.  Since  the  temperature  of  none  of  the 
particles  changes,  though  constantly  receiving  heat,  it  follows  that 
every  particle  transfers  just  as  much  heat  as  it  receives.  This  is 
the  permanent  stage  of  conduction,  and  the  facility  of  transfer  in 
this  state  is  what  is  usually  referred  to  as  conducting  power,  though, 
as  we  have  just  shown,  conduction  in  general  must  also  involve 
thermometric  conduction  or  diffusivity.  We  shall  hereafter,  in 
this  discussion,  for  brevity,  use  the  term  conductivity  to  refer  to 
the  permanent  stage  only.  It  is  independent  of  the  specific  heat 
of  the  body. 

Determination  of  Conductivity. — One  definition  of  temperature 
has  been  given  as  "  the  state  of  a  body  or  portion  of  matter  with 
respect  to  its  capacity  to  communicate  heat  to  other  matter." 
Conduction  is  the  process  by  which  heat  is  communicated  to  con- 
tiguous matter,  and  to  determine  conductivity  we  must  measure  the 
flow  of  heat  in  a  unit  of  time,  in  the  permanent  state,  due  to  the 
difference  of  temperature  which  produces  it. 

The  conductivity  of  a  body  is  usually  defined  as  the  amount  of 
heat  which  flows  through  a  plate  of  unit  area  and  of  unit  thickness 
in  a  unit  of  time  when  there  is  a  unit  difference  of  temperature 
between  the  sides.  If  we  had  a  plate  of  unit  area,  of  unit  thick- 
ness, and  could  keep  a  unit  difference  of  temperature  between  the 
sides,  and  should  then  determine  the  quantity  of  heat  passing 
through  it  in  a  given  time,  we  should  have  an  obvious  means  of 
determining  its  conductivity.  But,  for  reasons  which  will  subse- 
quently appear,  this  simple  and  direct  means  of  determining  the 
flow  of  heat,  and  thereby  the  conductivity,  cannot  be  employed. 

The  measure  of  the  passage  of  heat  by  conduction  after  the 
body  has  reached  the  permanent  state  has  to  be  made  in  a  more 
indirect  way.  One  of  the  simplest  methods  and  most  important  in 
practice  is  by  observation  of  the  permanent  distribution  of  tem- 
perature in  a  cylindrical  mass  of  the  body,  one  end  of  which  is 


CONDUCTION. 


69 


subjected  to  a  constant  source  of  heat  while  the  rest  of  the  surface 
is  cooled  by  exposure  to  lower  temperature. 

This  method,  employed  by  Forbes  with  iron,  will  make  plain 
the  principles  involved,  A  bar  of  iron,  mounted  as  in  Fig.  35,  was 
kept  at  a  constant  temperature  at  one  end,  molten  lead  being  used 
for  the  purpose.  The  bar,  in  the  experiment  here  described,  was 
3  feet  long  and  of  square  section  1J  inches  on  a  side.  The  entire 


FIG.  35.— DETERMINATION  OF  CONDUCTIVITY. 

surface  of  the  bar,  except  the  heated  end,  was  exposed  to  the  air. 
Holes  were  drilled  in  the  bar  and  thermometers  inserted  at  different 
points,  metallic  connection  between  the  bar  and  the  thermometer- 
bulbs  being  secured  by  inserting  a  few  drops  of  mercury  or 
amalgam.* 

After  a  sufficient  lapse  of  time  the  bar  arrived  at  the  permanent 
state,  and  the  thermometers  showed  a  gradual  decrease  of  tempera- 
ture from  the  heated  end  outward.  The  farther  end  was  not  sensi- 
bly raised  in  temperature.  It  is  evident  that  by  this  means  the 
distribution  of  temperature  along  the  bar  could  be  obtained.  If 
we  deduct  the  temperature  of  the  atmosphere  from  that  of  the 
various  points  of  the  bar,  we  shall  know  the  excess  of  temperature 
of  these  points  of  the  bar  above  that  of  the  atmosphere.  These 
numbers  may  be  used  as  the  ordinates  of  a  curve  which  will  indi- 
cate the  excess  of  temperature  along  the  bar,  above  that  of  the 
atmosphere,  the  axis  of  the  bar  forming  the  axis  of  abscissas.  This 

*  General  considerations  of  the  problem  of  conduction  demonstrate  that 
the  temperature  is  practically  the  same  throughout  each  cross-section  of  the  bar. 


70 


ELEMENTARY  LESSONS  IN  HEAT. 


curve  will  represent  this  excess  the  more  accurately  the  greater  the 
number  of  points  at  which  the  temperature  of  the  bar  is  deter- 
mined. The  curve  will  intersect  the  axis  of  the  bar  at  the  point 
at  which  the  temperature  of  the  bar  is  the  same  as  that  of  the 
atmosphere, — at  the  point  at  which  the  effects  of  the  source  of 
heat  cease  to  be  felt  in  the  bar. 

Let  CD By  Fig.  36,  represent  such  a  curve  of  temperature. 
Since  the  bar  has  reached  the  permanent  state,  it  is  clear  that  all 
the  heat  which  crosses  any  section,  as  ef,  passes  into  the  air  by 
radiation  and  convection.  We  shall  know  then  the  amount  of  heat 


FIG.  36.— CURVE  OF  TEMPERATURE. 

which  is  conducted  across  any  section,  ef,  of  the  bar,  in  any  time, 
if  we  can  determine  the  amount  of  heat  given  off  in  the  same  time 
from  the  portion  of  the  bar  beyond  that  section. 

By  actual  experiment  on  a  similar  bar,  heated  to  a  high  temper- 
ature and  subjected  to  the  same  atmospheric  conditions  as  the  first, 
the  determined  rate  of  cooling  would  enable  us  to  calculate  the 
amount  of  heat  lost  by  this  bar,  per  unit  of  length,  per  unit  of 
time,  at  each  temperature  within  the  range  employed.  This  knowl- 
edge would  enable  us  to  calculate  the  loss  in  a  given  time  in  any 
portion  of  the  other  experimental  bar,  since  we  know  the  stationary 
distribution  of  temperature  in  it  from  the  curve  of  excess.  This 
was  the  method  adopted  by  Forbes.* 

*  Forbes  determined  the  heat  given  out  by  his  second  bar  in  cooling  by  the 
fall  of  temperature  in  the  bar  itself;  and  by  calculating  the  specific  heat  of  the 
bar  per  unit  of  volume  (from  the  specific  gravity  and  specific  heat)  he  obtained 
the  actual  quantity  of  heat  given  out. 


CONDUCTION.  71 

By  thus  being  able  to  determine  the  heat  given  off  in  any  time 
by  any  assigned  portion  of  the  bar,  we  are  enabled  to  know  the 
quantity  of  heat  which  passes  in  the  same  time  through  any  section; 
and  by  comparing  this  quantity  with  the  rate  of  diminution  of 
temperature  per  unit  of  length  along  the  bar  as  shown  by  the  tem- 
perature curve,  we  ascertain  the  conductivity  of  the  bar  at  the  tem- 
perature of  the  section,  or  the  flow  of  heat  due  to  the  difference  of 
temperature  which  produces  it. 

In  this  comparison  of  the  flow  of  heat  with  the  decrement  of 
temperature,  it  is  assumed  that  the  flow  of  heat  is,  first,  directly 
proportional  to  the  difference  of  temperature  between  the  sides  of 
the  section  considered,  and,  second,  inversely  to  the  distance  be- 
tween them.  This  first  assumption  is  in  accord  with  all  experi- 
ments for  small  differences  of  temperature,  and  is  probably  true  at 
all  temperatures,  but  neither  it  nor  the  second  assumption  has  been 
fully  verified  by  experiment.  Peclet's*  experiments  are  sometimes 
quoted  as  a  verification,  but  they  cannot  be  fairly  taken  as  such. 

Making  this  assumption,  and  denoting  by  Q  the  quantity  of  heat 
which  flows  through  any  section,  x  its  thickness,  v  and  v'  the  tem- 
peratures of  the  two  sides,  s  the  area  of  the  section,  and  t  the  time, 
we  may  write  generally 


in  which  Tc  is  the  conductivity  and  depends  on  the  material  experi- 
mented with;  and  if  s  and  t  equal  unity  we  have 


Now,  by  reference  to  the  temperature  curve  it  is  seen  that  - 

35 

is  the  tangent  of  the  angle  which  the  downward  slope  of  the  tem- 
perature-curve makes  with  the  axis  of  the  bar.  From  the  above  we 
have 


*  Annales  de  Chimie  et  de  Physique,  tome  2,  3me  serie. 


72  ELEMENTARY  LESSONS  IN  HEAT. 

This  value  of  k,  by  Forbes's  method,  is  given  entirely  in  terms 
obtained  by  experiment,  and,  if  the  sections  of  the  bar  could  be 
taken  continuously,  we  might  write 


1C  —  -=-. 

dv 
dx 

//?J 

in  which  -=-  is  the  rate  of  decrement  of  the  temperature  along  the 

bar,  or  the  tangent  of  the  temperature  gradient  at  any  point,  but, 
since  such  a  continuous  result  can  only  be  obtained  by  computa- 
tion, the  value  of  k  must  depend  partly  on  the  assumptions  above 
given. 

It  is,  however,  to  be  observed  that  conductivity  must  be  deter- 
mined by  the  quantity  of  heat  which  passes,  and  that  this  can  only 
depend  npon  the  nature  and  dimensions  of  the  body  and  the  differ- 
ence of  temperature  between  its  parts,  and  these  all  enter  the 
expression  for  the  value  of  k,  and  that,  although  this  value  depends 
partly  on  the  assumptions  given  above,  it  is  at  the  same  time  possi- 

v  —  v* 
ble  from  the  experimental  values  of  Q,  -  (or  passing  to  the 

\jC 

limit  -=-)  to  ascertain  the  correctness  of  the  assumptions  themselves, 

CtX 

and  also  to  ascertain  whether  k  varies  with  the  temperature.  It  is 
plain  that  by  using  different  substances  their  conductivity  may  be 
similarly  determined. 

It  will  now  be  evident  why  the  direct  method  of  determining 
absolute  conductivity,  suggested  by  the  definition,  cannot  be  fol- 
lowed. The  curve  of  temperature  within  a  body  is  determined  b}^ 
the  mutual  influences  of  the  temperature  conditions  to  which  all 
the  different  parts  of  the  body  are  subjected,  and  it  is  entirely  im- 
possible to  fix  arbitrarily  the  temperatures  of  different  parts  of  a 
body  by  bringing  these  parts  into  contact  with  other  bodies  at  dif- 
ferent determined  temperatures.  Under  the  influence  of  the  first 
body  the  temperatures  of  the  applied  bodies  are  changed,  which 
change  is  further  increased  by  their  action  on  each  other  through 
the  medium  of  the  first  body,  so  that  the  temperature  of  no  two 
parts  of  a  body  at  different  temperatures  can  be  fixed  arbitrarily, 
but  must  be  known  from  experiment.  If  the  applied  temperature 


CONDUCTION.  73 

conditions  to  which  a  body  is  subjected  are  permanent,  it  will  itself 
reach  the  permanent  state,  and  its  temperature  curve  can  then  be 
known  by  experiment  only. 

The  expression  Q  —  ks 1, 

*c 

is  frequently  said  to  give  the  flow  of  heat  through  a  substance  when  the  con- 
ductivity is  k,  the  area  s,  thickness  x,  and  the  time  t,  when  the  two  sides  are 
kept  at  the  temperatures  v  and  v  and  when  there  is  no  heat  lost  laterally.  This 
last  condition  may  be  practically  attained  by  having  the  area. so  great  that  the 
lateral  loss  is  insignificant  when  compared  with  that  which  passes  transversely, 
or  the  lateral  loss  may  also  be  made  insignificant  by  proper  coverings.  The 
other  condition  of  the  problem  is  clearly  impossible :  the  faces  cannot  be  kept 
at  v  and  v',  but  will  assume  temperatures  depending  upon  the  temperatures  of 
the  bodies  contiguous  to  and  near  them.  The  discussion  of  such  a  problem  is 
accordingly  not  only  useless  but  misleading,  and  has  caused  a  great  deal  of 
confusion  in  the  discussion  of  this  subject.  A  proper  statement  of  the  relations 
implied  in  the  above  equation  is  that  it  gives  the  quantity  of  heat  which  flows 
through  any  section  whose  area  is  s,  and  thickness  x,  in  the  time  t,  when  the 
two  sides  of  the  section  assume  the  temperatures  v  and  v'  under  the  conditions 
of  the  experiment.  The  conductivity  through  any  section  under  these  condi- 
tions being  determined,  the  conductivity  through  a  given  thickness,  with  a 
given  difference  of  temperature  between  the  sides,  must  be  computed  from  the 
assumptions  already  referred  to. 

Determination  of  Diffusivity.— -It  one  part  of  a  body  be  subjected 
to  periodic  variations  of  temperature  and  the  periodic  variations  at 
other  points  be  observed,  the  diffusivity  of  the  body  may  be  calcu- 
lated. The  explanation  of  the  method  is  not  deemed  appropriate 
in  the  present  work. 

When  the  diffusivity  is  known  and  the  specific  heat  per  unit  of 
volume  also  known,  the  conductivity  is  given. 

Absolute  and  Relative  Conductivity.— The  absolute  conductivity 
of  wrought  iron,  from  the  determinations  of  Forbes,*  Tait,f 
Angstrom,!  and  Neumann,§  may  be  taken  as  0.20.  The  absolute 
conductivity  of  copper,  from  the  determinations  of  the  two  experi- 

*  Phil.  Trans.  R.  8.  E.,  vol.  xxiii. 

|R.  S.  E.,  1878. 

t  Phil.  Mag. ,  September,  1863. 

§  Annales  de  Chim.  et  de  Phys. ,  3me  serie,  tome  66. 


74 


ELEMENTARY  LESSONS  IN  HEAT. 


menters  last  named,  may  be  taken  as  1.0.  In  the  above  numbers 
the  0.  G-.  S.  scale  is  employed,  and,  considering  copper,  is  equiva- 
lent to  saying  that  heat  sufficient  to  raise  a  gramme  of  water  one 
degree  C.  in  temperature  will  pass  through  a  plate  of  the  metal  one 
centimetre  square  and  one  centimetre  thick  in  one  second  of  time, 
when  the  two  surfaces  differ  in  temperature  by  one  degree,  the 
copper  having  reached  the  permanent  stage  as  above  described. 

The  conductivity  of  iron  was  found  to  diminish  as  the  temper- 
ature increased,  and  according  to  Tait  it  is  at  a  minimum  some- 
where about  red  heat.  According  to  the  same  authority,  iron  is  an 
exception  in  this  respect,  the  majority  of  the  metals  improving  in 
conductivity  with  rise  of  temperature.  The  following  table  gives 
the  approximate  relative  conductivities  of  the  metals  named,  copper 
being  taken  as  100 : 


Copper 100 

Silver 135.9 

Gold..  72.1 


Tin 19.8 

Lead 11.5 

Platinum..  8.7 


The  absolute  conductivity  of  copper  being  known,  we  may  from 
this  table  of  relative  conductivities  calculate  the  absolute  conduc- 
tivities of  the  other  metals. 

From  the  absolute  conductivities,  the  diffusivities  may  be  com- 
puted by  dividing  by  the  thermal  capacity  per  unit  of  volume. 
Denoting  the  absolute  conductivity  by  k,  and  the  thermal  capacity 

k 

per  unit  of  volume  by  c,  the  diffusivity  is  — ;  c  is  obtained  by  mul- 

c 

tiplying  together  the  specific  heats  and  specific  gravities  of  the 
respective  metals. 

Conductivity  of  Solids. — As  a  class  the  solids  are  the  best  con- 
ductors, and  among  these  the  metals  stand  first,  stone  second,  and 
wood  third. 

The  difference  in  the  conducting  power  of  substances  explains 
many  familiar  phenomena.  If  we  enter  a  room  the  temperature  of 
which  is  below  that  of  our  bodies,  and  place  the  hand  upon  different 
articles  in  the  room,  different  sensations  of  cold  will  be  experienced; 
on  the  other  hand,  if  the  temperature  of  the  room  be  above  our 
own  temperatures,  some  of  the  bodies  will  appear  warmer  than 
others,  though  in  each  instance  the  bodies  in  the  room  are  at  one 


CONDUCTION.  75 

temperature, — that  of  the  room.  In  the  first  case  it  is  the  better 
conductors  which  feel  colder,  and  in  the  second  they  feel  warmer, 
the  difference  being  due  to  the  facility  with  which  they  take  heat 
from  and  give  it  to  our  bodies. 

The  knowledge  of  the  relative  conducting  powers  of  substances 
is  important  in  many  practical  applications.  In  our  houses  the 
material  and  thickness  of  the  walls  must  be  considered  both  for 
economy  and  comfort.  The  walls  should  be  of  non-conducting 
material,  both  for  keeping  them  warm  in  winter  and  cool  in  sum- 
mer. Wood  and  brick  are  poorer  conductors  than  stone. 

Conducting  Power  of  Liquids. — With  the  exception  of  mer- 
cury and  molten  metals,  liquids  are  very  poor  conductors.  This 
can  be  shown  in  a  very  simple  way  by  heating  the  upper  part  of  a 
column  of  liquid  and  observing  the  variations  of  temperature  below, 
which  will  be  exceedingly  slow  and  scarcely  perceptible.  Water 
may  be  placed  in  a  test-tube  over  a  piece  of  ice  held  down  by  a 
small  weight,  and  the  upper  portion  of  the  tube  may  be  heated  and 
the  water  boiled  for  a  considerable  time  without  melting  the  ice 
below.  Of  a  large  number  of  substances  liquid  at  ordinary  tem- 
peratures, Guthrie  determined  that  water  had  the  greatest  conduct- 
ing power.*  The  absolute  conductivity  of  water  as  determined  by 
Bottomley  is  greater  than  that  of  wood,  and  about  ?i¥  that  of 
copper. 

Conducting  Power  of  Gases.— The  conducting  powers  of  gases 
are  very  feeble  and  difficult  of  measurement.  It  is,  however, 
possible,  assuming  the  kinetic  theory  of  gases,  to  calculate  con- 
ducting powers  with  perhaps  more  accuracy  than  they  can  be 
determined  by  experiment.  We  know  that  all  gases  are  exceed- 
ingly bad  conductors,  and  wherever  gases  are  enclosed  in  small 
cavities  so  as  to  prevent  their  circulation,  the  system  produced  is  a 
bad  conductor.  This  is  the  cause  of  the  feeble  conducting  power 
of  furs,  eider-down,  felt,  and  loose  woollen  and  cotton  cloths. 
Materials  of  this  kind  when  used  for  clothing  are  warm  because 
they  prevent  the  escape  of  heat  from  the  body.  If  a  garment  of 
down  or  fur  be  pressed  flat  so  as  to  remove  the  air,  it  will  be  a  much 
better  conductor  and  less  warm. 

*  Trans.  R.  S. 


76  ELEMENTARY  LESSONS  IN  HEAT. 

The  snow  which  often  covers  the  earth  in  cold  climates  has  ^ir 
nearly  immovably  imprisoned  within  its  flakes,  and  is  an  excellent 
non-conductor  of  heat.  Snow  thus  often  protects  the  rootlets  which 
would  otherwise  freeze  and  prevent  perennial  vegetation.  The 
conducting  power  of  hydrogen  is  superior  to  that  of  other  gases, 
and  about  seven  times  that  of  the  air,  and  that  of  the  air  is  about 
^^  that  of  copper. 

Notwithstanding  the  poor  conducting  power  of  gases  and 
liquids,  we  know  that  they  can  be  cooled  and  warmed  very  readily. 
This  is  due  to  the  fact,  already  mentioned,  that  they  expand  by 
heat  and  rise,  while  the  colder  fluid  descends,  and  thus  are  estab- 
lished the  convection  currents  previously  discussed. 

From  the  above  principles  it  is  evident  that,  if  a  fluid  be  heated 
at  the  upper  surface  or  cooled  at  the  lower,  variation  of  temperature 
away  from  these  surfaces  will  take  place  very  slowly.  An  air- 
space is  thus  often  made  an  immense  protection  to  upper  rooms 
from  the  sun's  heat. 


CHAPTER  VIII, 
RADIATION. 

IN  conduction  a  transfer  of  heat  takes  place  between  contiguous 
particles  of  matter.  Radiation  is  the  process  by  which  a  transfer 
takes  place  between  bodies  not  in  contact.  Thus  considered,  radia- 
tion consists  of  three  distinct  phenomena, — emission,  transmission, 
and  absorption ;  and  three  bodies  are  concerned, — the  body  from 
which  the  heat  passes,  that  through  which  it  passes,  and  that  to 
which  it  passes. 

Radiation  Distinct  from  Conduction. — In  conduction  the  spread 
of  heat  to  points  remote  from  the  source  can  only  take  place  by  the 
warming  of  the  intervening  medium,  so  that  any  portion  of  the 
medium  is  at  higher  temperature  than  all  other  portions  more 
distant  from  the  source.  In  radiation  no  elevation  of  temperature 
of  the  intervening  medium  seems  essential  to  the  transfer  of  heat 
to  distant  bodies.  Radiation  takes  place  through  many  bodies 
without  sensible  elevation  of  temperature,  though  all  bodies  are 
probably  slightly  heated. 

Conduction  is  a  gradual,  while  radiation  is  an- almost  instan- 
taneous process.  The  heat  radiated  from  a  hot  body  to  another 
may  be  instantly  cut  off  by  a  screen,  and  resumes  its  full  intensity 
as  promptly  upon  the  removal  of  the  screen.  By  conduction  heat 
travels  from  the  hotter  to  the  colder  parts  of  the  medium,  whatever 
the  direction  be  ;  by  radiation,  in  a  homogeneous  medium,  the  heat 
travels  in  straight  lines. 

General  Properties  of  Radiant  Heat.— It  is  now  generally 
believed  that  both  radiant  heat  and  light  are  the  results  of  a  vibra- 
tory motion  which  is  transmitted  through  space  in  undulations  or 
waves  by  an  all-pervading  medium  called  luminiferous  ether;  and 
before  considering  radiant  heat  in  relation  to  the  physical  proper- 

77 


78  ELEMENTARY  LESSONS  IN  HEAT. 

ties  of  particular  substances,  we  shall  give  some  of  the  most  impor- 
tant general  properties  of  radiant  heat  as  determined  by  experiment. 

1.  Eadiant   heat  travels   through   a  vacuum   or  homogeneous 
medium  (with  an  exception  to  be  named)  in  straight  lines,  as  can 
be  readily  shown  by  means  of  opaque  screens. 

2.  From  a  heated  point  it  would  be  emitted  in  straight  lines 
equally  in  all  directions ;  hence  the  heat  energy  which  in  a  given 
time  falls  on  a  given  area  is  inversely  proportional  to  the  square  of 
the  distance  of  the  area  from  the  radiating  point.     The  velocity  of 
propagation  of  radiant  heat  has  not  been  directly  measured,  but 
there  is  the  strongest  possible  reason  for  believing  it  to  be  the  same 
as  that  of  light. 

3.  Radiant  heat  is  reflected  from  a  polished  surface,  and  the 
direction  of  the  reflected  ray  is  determined  by  fixp<3  laws  : 

FIRST. — The  reflected  ray  lies  in  the  plane  of  incidence.* 
SECOND. — The  reflected  and  incident  rays  make  equal  angles 
with  the  normal  to  the  surface  at  the  point  of  incidence. 

Owing  to  the  inequalities  of  even  the  finest  polished  surfaces,  a 
portion  of  the  reflected  heat  makes  with  the  normal  an  angle  dif- 
ferent from  the  incident  ray.  This  irregular  reflection  is  called 
diffusion  of  heat,  and  must  be  distinguished  from  the  phenomenon 
designated  under  conduction  by  the  term  diffnsivity. 

4.  In  addition  to  the  part  of  the  heat  which  is  regularly  and 
irregularly  reflected  from  the  incident  surface,  a  certain  quantity 
usually,  probably  always,  penetrates  the  second  medium :  of  the 
quantity  thus  entering  the  body  a  certain  proportion  is  always 
absorbed.     In  general,  if  the  incident  heat  is  not  normal  to  the  sur- 
face of  the  second  medium,  the  portion  which  penetrates  it  will 
undergo  refraction  or  be  bent  out  of  the  original  direction,  and  the 
refracted  ray  will  lie  in  the  plane  which  contains  the  incident  ray 
and  the  normal  to  the  surface  at  the  point  of  incidence. 

Theory  of  Exchanges. — Before  proceeding  to  describe  more  in 
detail  the  phenomena  attending  the  radiation  of  heat,  it  will  be 
well  for  the  student  to  understand  what  is  meant  by  the  Theory  of 
Exchanges.  This  theory  asserts  that  all  bodies  are  constantly 

*  The  plane  of  incidence  is  the  plane  passing  through  the  incident  ray  and 
the  normal  to  the  surface  at  the  point  of  incidence. 


RADIATION.  79 

giving  out  heat  by  -adiation,  at  a  rate  depending  upon  their  sub- 
stance and  temperature,  but  independent  of  the  substance  and  tem- 
perature of  the  bodies  surrounding  them  ;  and  that  whether  the 
body  remains  at  the  same  temperature  or  alters  its  temperature 
depends  upon  whether  it  receives  as  much  heat  from  other  bodies 
as  it  yields  up  to  them.  This  theory  is  now  generally  received, 
and,  while  affording  explanation  of  many  phenomena,  it  has  also 
suggested  new  truths  which  have  afterwards  been  experimentally 
verified. 

The  theory  is  frequently  called  Pre  vest's  theory,  after  its  author. 
It  has  been  developed  by  De  la  Provostaye,  Desains,  Kirchhoff,  and 
Balfour  Stewart.  The  last  named  has  made  a  very  satisfactory 
discussion  of  the  theory  in  his  Elementary  Treatise  on  Heat,  but  it 
cannot  be  sufficiently  condensed  for  insertion  here.  The  compre- 
hension of  the  theory  will  facilitate  the  conception  of  many  of  the 
principles  subsequently  involved,  and  it  will  conflict  with  none. 
Indeed,  the  theory  is  sustained  by  all  experimental  investigation  of 
the  subject  of  radiant  heat. 

The  general  properties  of  radiant  heat  thus  far  given  indicate 
its  similarity  to  light,  but  the  analogy  is  still  more  striking  when 
the  more  special  phenomena  attending  the  radiation  of  heat  are 
compared  with  the  corresponding  optical  phenomena.  Some  of 
these  we  now  proceed  to  give. 

Light  and  Heat  Spectra  of  Bodies. — If  a  beam  of  sunlight  be 
made  to  fall  obliquely  upon  the  side  of  a  glass  prism  whose  edge  is 
vertical,  two  phenomena  will  be  observed.  The  direction  of  the 
beam  will  be  changed  in  passing  through  the  prism,  and  it  will  no 
longer  be  white  light,  but  will  be  separated  into  its  constituent  colors. 
If  we  should  try  this  experiment  in  a  darkened  room  and  place 
behind  the  prism  a  screen,  we  should  find  an  oblong  space  on  the 


RED 

OR- 
ANGE 

Y£L 

LOW 

SREEN 

BLUE 

INDIOO 

VIOLET 

Fio.  37.— ORDER  OF  COLORS  IN  SPECTRUM. 


screen  illuminated  by  the  various  colors,  as  indicated  in  the  diagram 
Fig.  37.  All  these  colors  would  be  bent  out  of  the  original  direction 
of  the  beam,  the  red  least  and  the  violet  most.  In  this  case  the 
colored  space  is  called  the  solar  spectrum,  and  if  it  be  formed  from 


80  ELEMENTARY  LESSONS  IN  HEAT. 

any  other  body  it  is  the  spectrum  of  that  body.  The  spectrum  thus 
formed  is  but  a  series  of  overlapping  colored  images  of  the  slit  or 
opening  through  which  the  beam  of  light  passes,  due  to  the  unequal 
refraction  of  the  different  colors.  The  spectrum  may  also  be  formed 
by  a  reflecting  diffraction-grating,  this  grating  consisting  of  a  sys- 
tem of  close  equidistant  parallel  lines  ruled  on  glass  or  polished 
metal.  Such  a  spectrum  is  generally  designated  as  a  normal  spec- 
trum, and  in  it  the  positions  of  the  colors  are  determined  by  the 
corresponding  wave-lengths. 

In  the  normal  spectrum  the  maximum  heating  effect  does  not 
coincide  with  the  maximum  light  effect,  the  former  being  in  the 
orange-yellow  and  the  latter  in  the  yellow.  These  positions  vary 
slightly  with  the  extent  of  the  earth's  atmosphere  through  which 
the  heat  and  light  pass,  and  consequently  with  the  altitude  of  the 
snn.  The  above-given  are  for  the  sun  in  the  zenith.  The  heating 
effect  is  found  throughout  the  spectrum  and  for  a  short  distance 
beyond  the  violet  and  far  beyond  the  red  end. 

We  thus  see  that  the  grating  which  produces  the  light  spectrum 
also  produces  a  heat  spectrum,  extending  throughout  the  light 
spectrum  and  beyond  on  both  sides,  the  maximum  of  the  heat  effect 
being  near  the  red  of  the  spectrum.  With  the  spectra  of  the  other 
luminous  bodies  results  are  observed  analogous  to  those  here  given 
for  the  solar  spectrum. 

Refraction  of  Heat. — From  the  distribution  of  heat  in  the 
spectrum  as  above  described,  the  bending  of  the  heat  rays  out  of 
their  original  course,  or  refraction,  is  clearly  implied.  Melloni  first 
showed  in  a  more  direct  way  that  heat  from  a  non-lurninous  source 
was  capable  of  refraction.  By  using  a  lens  and  prism  of  rock-salt 
between  the  non-luminous  source  of  heat  and  the  thermopile,*  he 
showed  conclusively  that  the  heat  could  be  bent  out  of  its  course 
and  concentrated  to  a  point  in  the  same  manner  as  light.  Forbes 
showed  that  the  refrangibility  of  non-luminous  heat  was  less  than 
that  of  luminous  rays.  All  lenses  for  kindling  by  the  sun's  heat 
depend  upon  the  property  of  refraction. 

Reflecting  Power. — The  reflecting  power  of  a  surface  is  meas- 
ured by  the  proportion  of  the  incident  heat  which  is  regularly 

*  The  thermopile  is  an  instrument  giving  electrical  indication  of  very  slight 
changes  of  temperature,  and  capable  of  detecting  very  small  quantities  of  neat. 


RADIATION. 


81 


reflected  from  it.  This  property  of  substances  has  been  investigated 
by  Leslie,  Melloni,  Desains,  and  De  la  Provostaye.  The  first  named 
determined  the  relative  reflecting  power,  taking  brass  as  a  standard  ; 
the  three  last  named  determined  the  absolute  power.  It  was  shown 
by  Desains  and  De  la  Provostaye  that  for  diathermanous  substances, 
or  such  as  permit  heat  to  pass  through  them,  the  reflecting  power 
increased  as  the  angle  of  incidence  was  increased.  For  metals, 
which  do  not  transmit  heat,  the  reflecting  power  varied  very  slightly 
with  the  angle  of  incidence,  and  after  the  angle  had  reached  about 
75°  a  further  increase  caused  a  decrease  in  reflecting  power.  They 
also  show  that  the  reflecting  power  varied  with  the  source  of  heat. 
These  phenomena  are  entirely  analogous  for  light. 

Some  of  the  results  of  the  experimenters  last  named  are  here 
given  ;  the  source  of  heat  was  luminous,  an  oil  lamp  being  used. 


Silver-plate 0.97 

Gold 0.95 

Brass..  ..  0.93 


Speculum  metal. 

Zinc 

Iron 


0.86 
0.81 
0.77 


Burning  Mirrors. — This  reflecting  power  is  made  use  of  in 
all  burning  mirrors,  and  the  construction  of  such  mirrors  depends 
upon  the  laws  of  reflection  already  referred  to,  and  may  be  used  to 
verify  them.  All  rays  either  of  heat  or  light  falling  upon  a  properly 
constructed  concave  mirror  from  a  direction  parallel  to  its  axis  are 
reflected  to  its  focus.  Tschirnhausen's  mirror  which  was  con- 
structed in  1687  was  about  six  and  a  half  feet  in  diameter,  and  was 
capable  of  fusing  copper  and  silver.  Instead  of  curved  mirrors, 
plane  movable  ones  may  be  so  arranged  as  to  converge  their 
reflected  rays  to  a  point  and  thus  produce  a  powerful  effect.  Such 
was  the  reported  arrangement  by  which  Archimedes  is  said  to  have 
destroyed  the  Roman  fleet  in  the  siege  of  Syracuse. 

Irregular  Reflection  of  Heat. — The  irregular  reflection  of  heat 
which  is  designated  diffusion,  and  probably  resulting  as  previously 
described,  is  often  felt  very  strongly  from  a  white  wall  or  other 
white  surface  exposed  to  the  direct  rays  of  the  sun.  That  this  heat 
cannot  be  due  to  radiation  from  the  heated  surface  is  shown  by  the 
fact  that  it  instantly  attains  its  maximum,  instead  of  rising  gradu- 
ally as  it  would  if  it  were  radiated  from  the  body.  Moreover,  the 
heat  thus  diffused  from  bodies  in  direct  sunlight  always  agrees  in 


82 


ELEMENTARY  LESSONS  IN  HEAT. 


properties  with  the  heat  from  a  highly-heated  source,  which  could 
not  be  the  case  if  it  were  radiated  from  the  body  at  its  actual  tem- 
perature. The  irregular  reflection  of  heat  and  of  light  take  place 
in  the  same  manner,  and  the  laws  in  the  two  cases  so  far  as  they 
are  known  are  analogous. 

Emissive  Power. — It  is  a  familiar  fact  that  the  hotter  a  body 
is  the  more  heat  it  emits,  but  temperature  is  not  the  only  condition 
which  affects  the  quantity  emitted.  It  was  observed  by  Leslie  in 
1804  that  different  substances  have  very  different  emissive  powers 
even  at  the  same  temperature,  and  he  compared  the  emissive  powers 
of  various  substances  by  a  method  similar  but  less  perfect  than  the 
one  now  to  be  described. 

Melloni  determined  the  relative  emissive  powers  of  a  number  of 
substances  for  dark  heat  by  means  of  the  thermopile  (already 
referred  to)  and  a  cube  filled  with  water  kept  at  the  boiling  point, 
and  having  its  different  faces  covered  with  differences  substances. 
The  relative  emissive  powers  of  the  different  substances  were  given 
by  the  electrical  currents  produced  in  the  thermopile  when  the 
respective  faces  of  the  cube  were  allowed  to  radiate  heat  to  it,  these 
currents  being  indicated  by  the  deflections  of  a  galvanometer  needle 
in  circuit  with  the  pile. 

By  similar  means  De  la  Provostaye,  Desains,  Tyndall,  and  others 
have  also  made  determinations  of  this  power  in  different  bodies. 
The  relative  emissive  powers  of  the  non-metallic  substances  named 
below  are  from  the  determinations  of  Leslie  and  Melloni.  Those  of 
the  metals  were  determined  by  Desains  and  De  la  Provostaye. 


Lamp-black 100 

White  lead 100 

White  paper 98 

Crown  glass 90 


Polished  silver 2.5 

Gold-leaf 4.3 

Copper  foil 4.9 

Polished  platinum 9.2 


It  was  found  that  the  radiating  power  of  the  same  substance 
varied  with  the  condition  of  the  surface,  whether  it  was  polished, 
rough,  or  tarnished.  In  general,  the  more  dense  and  compact  the 
surface  of  the  body,  the  smaller  its  emissive  power,  and  polishing 
only  seemed  to  diminish  the  emissive  power  when  it  affected  the 
density  of  the  surface  layer. 

The  thickness  of  the  radiating  layer  was  also  found  to  exert  an 


RADIATION.  83 

influence  on  the  quantity  of  heat  emitted  at  a  given  temperature 
from  such  substances  as  were  perceptibly  transparent  to  heat  and 
therefore  gave  off  heat  from  particles  below  as  well  as  at  the  surface. 
For  bodies  which  are  practically  opaque  to  heat,  as  metals,  the 
effect  of  variation  of  thickness  was  imperceptible. 

Absorption  of  Radiant  Heat. — When  radiant  heat  falls  upon 
a  body,  whatever  portion  of  it  is  not  regularly  or  irregularly 
reflected  penetrates  the  substance  of  the  body ;  this  penetrating 
portion  may  be  partially  transmitted  through  the  body  without 
affecting  its  temperature,  or  it  may  be  partially  or  wholly  taken  up 
in  the  body  with  increase  of  temperature.  The  portion  which  is 
stopped  in  the  body  is  called  absorbed  heat.  In  bodies  which  are 
opaque  to  heat  absorption  like  emission  is  a  surface  action,  but  in 
diathermanous  bodies  it  takes  place  below  the  surface.  Experiment 
proves  that  different  substances  have  different  absorbing  powers,  and 
that  those  which  have  the  greatest  emissive  powers  have  also  the 
greatest  absorbing  powers :  the  correspondence  is  not  only  general 
but  exact;  the  numbers  which  express  the  radiating  powers  also 
express  the  absorbing  powers,  and  what  affects  the  one  affects  the 
other.  It  is  also  found  that  the  absorbing  power  of  the  same  sub- 
stance varies  with  the  source  of  heat.  From  the  above  statement 
in  regard  to  the  relation  existing  between  the  reflected  heat  and 
that  which  penetrates  the  body,  it  is  evident  that  a  good  absorber 
must  be  a  bad  reflector  and  a  good  reflector  a  bad  absorber  of  heat ; 
and  experiment  proves  such  to  be  the  case.  The  numbers  which 
have  been  given  for  the  emissive  powers  also  indicate  the  relative 
absorbing  powers  of  the  same  substance. 

Diathermancy,  or  the  Transmission  of  Heat. — We  have  above 
stated  that  of  the  heat  which  falls  upon  a  body  a  portion  is  reflected, 
regularly  or  irregularly,  and  the  remainder  enters  the  body.  The 
portion  which  enters  the  body  may  be  entirely  absorbed,  or  par- 
tially absorbed  and  partially  transmitted.  Diathermancy  refers  to 
the  power  which  bodies  have  of  transmitting  heat :  it  corresponds 
to  the  property  of  transparency  for  light. 

It  has  long  been  known  that  some  of  the  heat  from  an  intensely 
luminous  source,  as  the  sun,  could  pass  through  certain  transparent 
substances,  as  glass,  but  it  was  not  known  that  this  was  the  case 


ELEMENTARY  LESSONS  IN  HEAT. 


•with  heat  from  a  non-luminous  or  feebly  luminous  source.  Pictet 
was  the  first  to  establish  the  fact  of  diathermancy  for  radiant  heat 
in  general,  and  Prevost  proved  that  it  could  not  possibly  be  due  to 
absorption  and  subsequent  radiation  by  showing  that  such  heat 
passed  through  ice.  Many  investigations  have  been  made  as  to 
this  property  of  bodies,  and  some  of  the  more  important  conclu- 
sions are  here  given. 

Effect  of  Source  of  Heat.— As  a  general  rule,  the  same  substance 
transmits  unequal  quantities  of  heat  when  the  source  of  heat  is 
varied,  the  amount  increasing  with  the  temperature. 

The  following  table,  from  the  results  of  Melloni,  shows  the  pro- 
portion transmitted,  out  of  100  rays,  from  the  different  sources : 


SOURCE  01 

*  HEAT. 

SUBSTANCE. 

Locatella's 
Lamp. 

Incandescent 
Platinum 
Wire. 

Copper  at 

400°. 

Copper  at 
100°. 

92 

92 

92 

92 

Calcium  fluoride  

78 

69 

42 

33 

Pl;itt>-irla.ss            •       ...         . 

39 

24 

6 

o 

Scicnity         

14 

5 

o 

o 

9 

2 

o 

0 

6 

0.5 

0 

0 

Rock-salt  is  seen  from  the  table  to  transmit  the  same  proportion 
from  each  source,  and  Melloni  concluded  that  it  was  perfectly  dia- 
thermanous ;  but  it  has  since  been  shown  that  such  is  not  the  case, 
and  that,  though  its  absorbing  power  is  in  general  small,  it  is  still 
perceptible,  and  in  particular  cases,  yet  to  be  referred  to,  it  is  very 
great. 

Influence  of  the  Nature  and  Thickness  of  the  Material. — From 
the  list  given  in  the  table  (which  is  from  a  much  more  extended 
one),  it  is  seen  that  from  the  same  Ljiirce  the  transmitting  powers 
of  different  substances  are  very  different,  and  that  for  substances 
equally  transparent  to  light,  as  rock-salt  and  alum,  the  transmitting 
powers  are  greatly  different.  The  transmission  of  heat  and  light, 
then,  in  general  are  apparently  not  connected,  and  one  cannot 
be  taken  as  a  measure  for  the  other ;  but  it  should  here  be  stated 


RADIATION,  85 

that,  if  the  transmission  from  a  distinct  and  separate  portion  of  the 
spectrum  be  considered,  then  a  substance  which  is  transparent  to 
the  light  (say  rqd)  of  that  portion  also  transmits  the  heat  of  the 
same  portion. 

With  successive  strata  of  the  same  material  and  thickness,  in 
general  the  amount  transmitted  by  the  first,  in  proportion  to  the 
amount  falling  upon  it,  is  less  than  with  the  succeeding  strata ;  or 
we  may  say  that  a  plate  of  given  material  in  general  exercises  a 
sifting  effect  upon  the  rays  of  heat,  and  that  such  sifted  rays  are 
then  better  fitted  to  pass,  and  do  pass  with  less  obstruction,  through 
a  plate  of  the  same  material.  The  effect  of  varying  thickness  is  in 
general  as  stated,  but  Masson  and  Jamin  have  shown  that,  if  the 
heat  of  a  separate  and  distinct  portion  of  the  spectrum  be  passed 
through  successive  strata  of  the  same  thickness  and  material,  the 
amount  transmitted  decreases  in  a  geometrical  progression  as  the 
thickness  increases  in  arithmetical  progression.  This  simple  law 
for  the  absorption  of  the  solar  heat  by  the  earth's  atmosphere  was 
assumed  more  than  a  century  ago,  and  has  until  recently  been 
generally  employed  to  determine  the  solar  constant, — that  is,  the 
amount  of  heat  which  would  fall  in  a  unit  of  time  upon  a  unit  of 
area  normally  exposed  at  the  earth's  surface  if  there  were  no  atmos- 
phere. The  recent  extended  and  valuable  labors  of  Prof.  Langley 
have  conclusively  shown  that  the  earth's  atmosphere  exerts  a 
remarkable  sorting  power  upon  the  solar  rays,  and  that  the  above 
simple  law  is  inapplicable  )o  the  case. 

Prof.  Tyndall  showed  that  a  solution  of  iodine  in  carbon  bisul- 
phide, though  very  opaque  to  light,  permitted  heat  to  pass  in  great 
quantity. 

Absorptive  and  Emissive  Powers  of  Gases.— It  has  been  deter- 
mined by  Tyudall  that  the  absorptive  powers  of  elementary  gases 
for  heat  from  sources  at  low  temperatures  are  less  than  those  of 
compound  ones ;  oxygen,  hydrogen,  and  nitrogen,  in  the  quantities 
experimented  upon,  exert  an  almost  inappreciable  effect,  while 
olefiant  gas  (C2H4)  exerts  about  one  thousand  times  as  much.  The 
absorptive  power  increases  with  the  density,  but,  in  case  of  high 
absorptive  power,  not  proportionally  to  it.  The  same  lack  of  con- 
nection between  transparency  for  light  and  for  heat  was  observed 
in  the  case  of  gases  as  has  been  referred  to  in  the  case  of  solids. 


86  ELEMENTARY  LESSONS  IN  HEAT. 

Thus  ammonia,  which  was  quite  transparent  to  light,  was  black  or 
opaque  to  heat,  while  chlorine  allows  heat  to  pass  more  freely  though 
much  less  transparent  to  light. 

The  absorptive  power  of  vapors  or  the  more  readily  condensable 
gases  was  even  greater  than  that  of  the  more  permanent  compound 
gases :  thus  the  power  of  ammonia  was  greater  than  that  of  olefiant 
gas,  and  carbon  bisulphide  and  alcohol  had  still  higher  powers.  The 
most  important  of  Tyndall's  conclusions  refer  to  the  vapor  of  water, 
which,  weight  for  weight,  transcends  all  other  gases  or  vapors  in 
heat-absorbing  power,  so  much  that,  according  to  him,  though 
amounting  on  the  average  to  less  than  one-half  of  one  per  cent,  of 
the  whole  atmosphere,  it  exerts  an  absorbing  action  many  times 
greater  than  the  air  through  which  it  is  diffused.* 

Tyndall  also  examined  the  emissive  power  of  gases,  and  found, 
as  in  the  case  of  solids,  that  the  best  absorbers  were  also  the  best 
radiators. 

Prof.  Langley  has  demonstrated  that  the  earth's  atmosphere 
exerts  a  much  greater  absorbing  power  on  the  solar  rays  than  was 
formerly  supposed,  so  much  so  that  something  more  than  one-third 
of  this  energy  is  absorbed  by  the  atmosphere  when  the  sun  is  in 
the  zenith.  According  to  him,  the  amount  of  heat  which  would  fali 
upon  a  normally  exposed  surface  of  a  square  centimetre  area  at  the 
earth's  surface  in  a  minute  if  there  were  no  atmosphere  is  three 
calories, — that  is,  it  would  raise  one  gramme  of  water  three  degrees 
in  that  time.  This  is  probably  the  most  accurate  determination 
yet  made  of  the  solar  constant. 

Prof.  Langley  has  also  shown  that,  contrary  to  the  general  opin- 
ion, the  longer  waves  of  solar  heat  are  more  readily  transmitted  by 
the  earth's  atmosphere  than  the  shorter  ones,  and,  consequently, 
the  dark  solar  heat  more  readily  than  the  luminous.  In  such 
greater  proportion  are  the  shorter  waves  absorbed  that  if  one  could 
be  above  our  atmosphere  the  sun  would  be  blue. 


*  The  determinations  of  Magnus  make  the  absorbing  power  of  water  vapor 
much  less  than  that  given  by  Tyndall.  The  results  of  Magnus's  determinations 
are  supported  by  the  investigations  of  Hoorweg  and  Dr.  Buff,  and  it  now  seems 
certain  that  Tyndall  greatly  overestimated  the  action  of  water  vapor.  An 
account  of  the  last-named  experiments  may  be  seen  in  Pogg.  Annalen  del 
Physik.,  Bd.  civ.,  clviii. 


RADIATION.  87 

Laws  of  Cooling. — In  determining  the  emissive  powers  of  sub- 
stances as  described,  it  is  evident  that  what  was  measured  was  not 
the  actual  amount  of  heat  emitted  in  a  given  time,  but,  according 
to  the  theory  of  exchanges,  merely  the  difference  in  the  rate  of  ex- 
change between  the  radiating  body  and  the  surrounding  objects, 
including  the  thermopile.  If  the  pile  gives  back  as  much  heat  to 
the  radiating  body  as  it  receives  from  it,  no  matter  how  much  this 
might  be,  the  method  of  observation  described  would  indicate  no 
emission  whatever.  By  varying  the  temperature  of  the  pile  it  is 
evident  that  the  indicated  emissive  power  could  be  made  to  vary 
while  the  absolute  quantity  of  heat  emitted  was  the  same,  or  by 
varying  the  temperature  of  both  body  and  pile  the  indicated  emis- 
sive power  would  remain  unchanged  while  the  actual  quantity  of 
heat  emitted  would  change.  It  is  plain,  then,  that  the  emissive 
powers  thus  determined  establish  no  apparent  relation  between  the 
temperature  of  the  radiating  bodies  and  the  absolute  amounts  of 
heat  emitted. 

Law  of  Dulong  and  Petit. — To  ascertain  whether  such  relation 
existed,  Dulong  and  Petit  determined  the  rate  at  which  the  same 
body  cooled  in  vacuo  when  its  initial  temperature  exceeded  that  of 
the  enclosure  by  different  known  amounts.  They  concluded  that 
the  rate  of  cooling  in  a  given  time  depends  not  only  upon  the  dif- 
ference of  temperature  between  the  radiating  body  and  the  sur- 
rounding objects,  but  also  upon  its  absolute  temperature,  and  that 
the  rate  of  cooling  for  a  constant  excess  of  temperature  increases  in 
a  geometrical  progression  as  the  temperature  of  the  enclosure  or 
surrounding  bodies  increases  in  an  arithmetical  progression,  and 
that  the  ratio  of  the  progression  is  constant  whatever  be  the  excess 
of  temperature. 

From  the  above  relations  Dulong  and  Petit  were  enabled,  in 
accord  with  Prevost's  theory,  to  express  the  dependence  of  the  rate 
of  cooling  of  a  heated  body  upon  its  temperature  and  its  excess  of 
temperature  over  that  of  the  enclosure.* 

*  The  form  of  the  equation  is  B  =  C(af  +  *  —  a6),  in  which  B  is  tne  rate  of 
cooling  ;  C  is  a  constant  depending  upon  the  mass,  extent  of  surface,  specific 
heat  and  emissive  power  of  the  body  ;  a  is  the  ratio  of  the  rate  of  cooling  when 
the  temperature  of  the  enclosure  is  1°  to  the  rate  when  it  is  0°,  the  excess  being 
the  same  in  the  two  cases  ;  6  is  the  temperature  of  the  enclosure ;  and  t  the  ex- 
cess of  temperature  of  the  heated  body  above  the  enclosure. 


88  ELEMENTARY  LESSONS  IN  HEAT. 

It  was  supposed  by  Newton  that  the  rate  of  cooling  of  a  heated 
body  was  directly  proportional  to  its  excess  of  temperature  over 
that  of  surrounding  bodies,  and  this  statement  constitutes  New- 
ton's law,  but  from  the  above  experiments  it  is  seen  not  to  be  true 
in  general.  However,  Newton's  law  is  sensibly  accurate  for  small 
differences  of  temperature  between  the  body  and  enclosure,  and  for 
differences  not  exceeding  15°  or  20°  corresponds  very  closely  with 
the  formula  when  the  temperature  of  the  enclosure  is  constant. 

This  law  of  Petit  and  Dulong  was  deduced  in  1817.*  Since 
that  time  experiment  has  shown  that  the  law  does  not  hold  for  all 
temperatures  of  the  radiating  body.  Ferrel  has  recently  shown 
that  the  same  is  true  of  the  expressions  of  the  law  of  radiation  as 
given  by  Stefan  (1879)  and  Weber  (1888),  and  that  for  higher  and 
lower  temperatures  a  change  is  necessary  in  the  value  of  the  con- 
stants in  the  expression  of  the  law  for  ordinary  temperatures. 

Interference,  Polarization,  and  Diffraction. — In  addition  to  the 
analogous  phenomena  attending  the  radiation  of  heat  and  light  al- 
ready referred  to,  there  are  others  even  more  important  in  establish- 
ing the  exact  relation  between  heat  and  light  and  the  exact  nature 
of  heat  energy.  We  here  merely  name  these  phenomena. 

Interference. — There  are  methods  by  which  two  rays  or  beams 
of  light  can  be  made  to  produce  darkness  ;  this  phenomenon  is  des- 
ignated interference  of  light.  Two  beams  of  dark  heat  can  also  be 
made  to  interfere  so  that  the  thermic  effect  of  the  two  beams  is  less 
than  of  one. 

Polarization. — It  is  also  known  that  a  ray  of  light  after  passing 
through  a  properly  prepared  plate  of  tourmaline  will  pass  through 
a  similar  plate  when  held  in  a  certain  position,  but  not  otherwise. 
This  modified  ray  is  said  to  be  polarized.  There  are  many  other 
ways  of  polarizing  light  with  results  similar  to  the  above.  Heat 
may  be  polarized  in  the  same  way  as  light. 

Diffraction. — When  light  passes,  under  certain  circumstances, 
by  an  opaque  body  or  through  a  narrow  aperture,  certain  luminous 
effects  are  produced  out  of  the  direct  line  of  the  rays.  Exactly 
similar  phenomena  have  been  observed  with  heat,  and  hence  we  see 
that  heat  can  be  diffracted  as  well  as  light. 

*  Ann.  de  Chimie,  ii.,  v'ii.,  p.  337. 


RADIATION.  89 

It  may  here  be  added  that  the  phenomena  just  mentioned  are 
the  strongest  supports  of  the  theory  that  radiant  heat  and  light  are 
the  results  of  a  vibratory  motion  of  an  elastic  medium,  and  that  the 
vibrations  take  place  in  directions  perpendicular  to  that  in  which 
the  undulations  advance, — that  is  to  say,  in  a  direction  transverse 
to  the  direction  of  the  ray. 

Distinction  between  Radiant  Heat  and  Light.— From  the  fore 
going  facts  of  this  chapter,  the  marked  analogy  between  radiant 
heat  and  light  is  evident,  and,  without  further  detailing  their  com- 
mon characteristics,  we  may  add  that  all  their  known  properties 
point  to  the  conclusion  that  there  is  no  difference  of  a  fundamental 
kind  between  them.  On  the  contrary,  all  investigations  combine 
to  prove  that  radiant  heat  and  light  are  the  results  of  the  same 
physical  agent,  the  distinction  between  them  being  subjective  rather 
than  objective.  This  agent  is  now  universally  believed  to  be  the 
moving  molecules  or  particles  of  the  body  in  which  the  phenomena 
of  heat  and  light  are  observed  to  exist,  and  the  condition  of  bodies 
as  regards  heat  and  light  depends  entirely  upon  the  vibratory  motion 
of  their  molecules.  We  have  seen  from  the  action  of  the  grating 
that  rays  exist  of  refrangibilities  much  greater  and  less  than  those* 
which  compose  the  light  spectrum,  and  with  the  normal  spectrum, 
the  least  refrangible  rays  extend  far  outside  the  red,  while  the  most 
refrangible  are  beyond  the  violet.  As  has  been  observed,  the 
greatest  heating  effect  at  the  earth's  surface  is  near  the  red,  but 
Langley  has  shown  that  above  the  earth's  atmosphere,  owing  to  the 
greater  absorption  of  the  more  refrangible  rays,  this  maximum  is 
transferred  towards  the  violet.  The  more  refrangible  rays  at  the 
violet  end  of  the  spectrum  and  beyond  have  the  property  of  acting 
more  readily  upon  certain  salts  of  silver,  and  the  chemical  effect  is 
here  a  maximum.  The  physical  distinction  between  these  different 
parts  of  the  spectrum  is  believed  to  be  one  solely  of  wave  length. 
The  dark  spectrum  beyond  the  red  and  violet  is  but  the  natural 
prolongation  of  the  luminous  one,  and  is  caused  by  wave  lengths 
which  do  not  affect  the  visual  organ,  while  those  lengths  which 
produce  light  do  affect  it.  When  the  heat-wave  length  is  greater 
than  0.000812  of  a  millimetre,  and  a  little  less  than  one-half  this 
length,  it  ceases  to  produce  luminous  effect,  though  the  heating 


90  ELEMENTARY  LESSONS  IN  BEAT. 

effect  in  the  first  instance  and  the  chemical  effect  in  the  second 
are  very  marked. 

Prof.  Laugley  has  shown  that  the  invisible  heat  spectrum,  of 
greater  wave  length  than  red  light,  is  many  times  the  width  of  the 
visible  spectrum, — as  much  as  twenty  times.  The  longest  heat- 
wave length  recognized  ten  years  ago  was  0.0015  millimetre,  but 
the  above-named  physicist  has  succeeded  in  measuring  lengths, 
from  the  sun  as  well  as  from  other  sources,  of  0.03  millimetre. 

A  body  at  a  low  temperature  emits  only  dark  heat.  As  the 
temperature  rises,  the  emission  of  dark  heat  becomes  more  ener- 
getic, and  at  the  same  time  more  refrangible  rays  are  given  off  ;  the 
luminosity,  to  the  human  eye,  begins  when  the  red  rays  appear  and 
goes  on  to  include  rays  of  other  colors.  Only  bodies  at  the  highest 
temperature  give  out  waves  of  all  lengths.  Generally  speaking, 
the  rays  which  constitute  the  visible  spectrum  are  the  more  trans- 
missible, the  extreme  rays  being  most  readily  absorbed  ;  but  this  is 
not  always  the  case,  for,  as  we  have  already  stated,  rock-salt  is 
nearly  as  transparent  to  the  ultra-red  from  the  sun  as  it  is  for  light, 
and  a  solution  of  iodine  in  carbon  bisulphide  is  very  transparent  to 
the  ultra-red  and  opaque  to  luminous  ones.  Rock-crystal,  pure 
qnartz,  is  very  transparent  to  the  ultra-violet  rays.  The  departure 
from  this  law  in  the  case  of  the  earth's  atmosphere  has  already  been 
noted. 

It  is  also  seen  from  the  foregoing  facts  that  the  same  substance 
stops  the  heat  and  light  rays  of  the  different  parts  of  the  spectrum 
unequally,  and  it  has  also  been  noted  that  certain  bodies  entirely 
stop  the  polarized  beam.  The  peculiarity  of  heat,  whether  of 
polarization  or  wave  length,  which  causes  different  rays  to  be  une- 
qually absorbed  is  termed  quality.  The  increasing  temperature  of 
a  body,  besides  developing  rays  of  increasing  refrangibility  or  of 
different  wave  lengths,  also  increases  the  quantity  of  each  particu- 
lar refrangibility,  so  that  the  higher  the  temperature  the  more 
energetic  the  radiation  of  every  degree  of  refrangibility. 

In  conclusion,  it  may  be  accepted  that  heat  and  light  are  but 
varieties  of  the  same  physical  agency ;  that  light  is  heat  which 
affects  our  sense  of  sight,  while  dark  heat  does  not  thus  affect  us.* 

*  Melloni  asserted  this  fact  as  far  back  as  1843,  but  it  was  not  generally  ac 
cepted  as  such  until  quite  recently. 


RADIATION,  91 

Selective  Emission  and  Absorption. —The  accepted  view  as  tb 
the  nature  of  the  heat  agent  enables  us  to  connect  together  the 
various  phenomena  which  come  under  this  head.  According  to 
this  view  a  hot  radiating  body  is  one  whose  molecules  are  in  rapid 
vibration,  and  different  bodies  have  different  periods  of  vibration, 
which  periods  alter  with  the  temperature,  so  that  shorter  periods 
are  included  at  higher  temperatures,  and  these  vibrations  are  com- 
municated to  the  luminiferous  ether  and  propagated  by  it  in  undu- 
lations in  all  directions.  Those  conditions  of  a  body  which  promote 
the  transfer  of  its  vibrations  to  the  ether  constitute  it  a  good  radia- 
tor, and  the  conditions  which  enable  a  body  to  take  up  the  vibra- 
tions from  the  ether  make  it  a  good  absorber.  If  the  particles  of  a 
body  can  execute  vibrations  of  only  certain  periods,  they  can  take 
up  or  give  out  only  that  particular  vibration ;  hence  we  have  a 
conceivable  explanation  of  selective  absorption  and  emission. 

A  direct  consequence  of  these  principles  is  that  bodies  are  opaque 
to  their  own  radiation.  Thus  Stewart  has  shown  that  rock-salt, 
which  is  nearly  transparent  for  most  sources  of  heat,  is  nearly 
opaque  if  another  piece  of  rock-salt  be  the  source  of  heat.  Glass 
readily  absorbs  heat  of  low  refrangibility,  such  as  is  emitted  by  non- 
luminous  bodies,  but  allows  the  luminous  heat  (light)  to  pass  almost 
uninterruptedly.  Accordingly,  glass  when  heated  emits  abundantly 
non-luminous  heat,  but  very  little  light.  Red  glass  absorbs  green 
light,  but  if  it  be  heated  to  a  high  temperature  it  will  give  out  in 
the  dark  the  same  color. 

It  has  been  shown  by  experiment  that  any  bodies  whatever, 
placed  in  a  highly-heated  furnace  and  allowed  to  acquire  the  tem- 
perature of  the  furnace,  will  not  alter  the  light  emitted  from  it. 
The  bodies  when  cold  may  be  opaque  or  transparent,  colored  or 
colorless,  yet  all  will  exhibit  the  same  color  in  the  furnace, — that 
of  the  furnace  itself.  This  is  explained  when  we  remember  that  a 
body  which  absorbs  certain  kinds  of  rays  emits  the  same  on  its  own 
account,  so  that  the  radiation  which  it  sends  to  the  eye  is  partly  its 
own  and  partly  that  transmitted  from  the  coals  behind,  and  the 
total  is  exactly  the  same  as  that  which  comes  from  other  portions 
of  the  fuel.  With  an  opaque  body  (such  as  polished  platinum)  this 
totality  will  be  in  large  part  due  to  reflected  heat,  but  the  result 
will  be  the  same  in  kind  and  amount  as  that  from  the  coals.  If 
these  bodies  be  taken  out  of  the  furnace,  they  will,  in  the  dark, 


92  ELEMENTARY  LESSONS  IN  HEAT. 

while  hot,  exhibit  the  tints  due  to  their  own  emissions.  A  black 
body  in  such  an  enclosure  would  have  the  same  tint  as  the  others, 
but,  being  both  non-reflective  and  nearly  opaque  to  visible  emana- 
tions, all  its  light  is  proper  to  itself,  and,  if  taken  out  of  the  furnace 
into  the  dark,  it  would  exhibit  the  tint  of  the  enclosure. 

The  vibrating  periods  of  gases  are  more  sharply  defined  than 
those  of  solids  or  liquids,  and  they  exhibit  a  more  perfect  equality 
of  selective  radiation  and  absorption.  The  vapor  of  sodium  stops 
completely  that  portion  of  light  which  corresponds  to  a  definite 
shade  of  yellow  produced  by  its  own  combustion,  and  thus  produces 
a  dark  line  in  the  yellow  of  the  solar  spectrum. 

Summary  and  Conclusions. — From  the  facts  of  this  chapter  we 
are  enabled  to  draw  the  following  conclusions: 

In  general,  good  radiators  are  good  absorbers  of  heat  and  bad 
reflectors.  Absorption  and  radiation  are  both  surface  actions  in 
the  case  of  bodies  which,  like  lamp-black,  are  nearly  opaque  to  heat, 
except  of  the  greater  wave  lengths ;  metals  are  also  practically 
opaque.  In  diathermanous  bodies  radiation  and  absorption  go  on 
in  the  interior  also,  so  that  a  thick  plate  absorbs  more  heat  than  a 
thin  one,  and,  at  the  same  temperature,  radiates  more. 

Bodies  when  cold  absorb  the  same  kind  of  rays  that  they  give 
out  when  hot.  Lamp-black  is  the  most  perfect  absorber  and  radi- 
ator, it  being  devoid  both  of  reflecting  and  diffusive  power.  Its 
absorbing  power  is  also  most  nearly  independent  of  the  source  of 
heat.  It  absorbs  all  rays  nearly  alike,  the  luminous  as  well  as 
the  dark  ones.  Lamp-black  is  accordingly  taken  as  the  standard 
surface  of  absorption,  absorbing  in  the  greatest  degree  every  variety 
of  ray  which  falls  upon  it.*  It  is  consequently,  also,  when  hot,  the 
typical  radiator,  giving  out  the  maximum  amount  of  heat  which 
any  substance  at  the  same  temperature  could  possibly  give  out; 
moreoyer,  it  gives  out  the  maximum  amount  of  each  kind  of  heat 
that  can  be  given  out  by  any  body  at  that  temperature.  A  heated 
body  at  first  gives  off  obscure  rays,  but  as  the  temperature  rises  a 
proportion  of  luminous  rays  are  emitted ;  the  ratio  of  the  luminous 
to  the  obscure  heat  rays  is  in  the  case  of  all  ordinary  sources  small. 


*  Prof.  Langley  has  recently  shown  that,  for  the  greater  wave  lengths  which 
he  has  succeeded  in  detecting,  lamp-black  ia  nearly  transparent. 


RADIATION.  93 

Tyndall  showed  that  with  the  electric  light  this  ratio  was  only  one- 
tenth.  Langley  showed  that  of  the  radiant  energy  from  an  ordi- 
nary Argand  gas-burner  only  2.4  per  cent  were  light,  and  when  the 
energy  consumed  in  heating  the  air  by  convection  currents  is 
considered,  it  is  probable  that  less  than  1  per  cent  of  the  total 
energy  of  the  burner  appears  as  light.  All  colored  substances  owe 
this  element  of  their  beauty  to  their  partial  behavior  with  refer- 
ence to  the  different  visible  rays,  and  the  popular  impression  which 
attributes  warmth  to  the  red  and  orange  tones  correctly,  though 
probably  unconsciously,  expresses  a  physical  fact. 

We  see  also  that  a  body  may  be  a  good  reflector  of  luminous 
heat  (light)  and  an  excellent  absorber  of  dark  heat;  white  lead  is 
a  body  of  this  kind.  Domestic  utensils,  as  tea-  and  coffee-pots, 
which  are  intended  to  retain  heat,  are  more  efficient  when  they 
have  polished  metallic  surfaces;  while  the  outside  of  stoves  should 
be  black,  and  apparatus  for  heating  by  radiation  should  not  be  of 
polished  metal,  as  is  frequently  the  case  with  hot-water  apparatus. 
Fireplaces  should  be  lined  with  fire-brick  to  radiate  heat  into  the 
room,  at  the  same  time  keeping  up  the  temperature  of  the  fire. 
Glass  screens  transmit  the  light  from  the  fire  but  intercept  the 
larger  part  of  the  dark  heat;  glass  for  the  same  reason  is  efficient 
in  conservatories. 

Kadiation  and  conduction  are  the  only  processes  by  which  heat 
as  such  ever  leaves  a  body,  and  while  there  is,  as  we  have  pointed 
out,  a  distinction  between  the  processes,  their  ultimate  effect  is  the 
same, — viz.,  to  reduce  all  bodies  to  the  same  temperature. 


CHAPTER    IX. 
THERMO-DYNAMICS. 

Thermo-dynamics  is  that  branch  of  science  which  treats  of  the 
relations  of  heat  to  other  forms  of  energy. 

We  are  here  principally  concerned  with  the  relations  between 
heat  and  mechanical  effect.  That  heat  can  be  made  to  produce 
work  is  a  fact  familiar  to  all.  Indeed,  heat  is  through  engines  the 
most  important  source  of  mechanical  power  that  we  possess. 

Many  familiar  facts  also  supply  us  with  illustrations  of  the  pro- 
duction of  heat  by  the  expenditure  of  mechanical  energy.  Some 
examples  are  here  given. 

Heat  by  Friction. — The  common  method  of  lighting  a  match 
by  friction  is  one  of  the  simplest  illustrations  of  this  conversion  of 
mechanical  energy  into  heat.  Formerly  the  American  Indians,  by 
rapidly  rotating  a  small  rod  of  wood  while  pressing  it  firmly  against 


FIG.  38.— HEAT  BY  FRICTION. 


a  depression  in  another  piece,  managed  to  ignite  fine  dry  shavings 
and  thus  kindle  their  fires.  Other  savages  are  said  to  accomplish 
a  similar  result  in  a  similar  manner. 

94 


THERMODYNAMICS.  95 

An  experiment  of  TyndalPs  illustrates  the  same  principle.  He 
mounted  a  small  tube  (Pig.  38),  so  that  it  could  be  rapidly  rotated 
about  its  axis;  when  filled  with  water  and  closed  by  a  cork  and 
rapidly  rotated,  while  pressed  between  two  pieces  of  wood  covered 
with  leather,  the  cork  was  blown  out  by  the  steam  developed  by 
the  heat  due  to  the  friction.* 

In  the  year  1798  Count  Rumford  published  results  of  experi- 
ments as  to  the  large  amount  of  heat  produced  by  friction  in  the 
boring  of  cannon.  He  called  attention  to  the  fact  that  the  source 
appeared  "evidently  to  be  inexhaustible,"  and  argued  that  any- 
thing which  could  under  the  conditions  be  thus  furnished  without 
limitation  could  not  be  a  "  material  substance."  And  he  declared 
it  "  extremely  difficult  if  not  impossible  to  form  a  distinct  idea  of 
anything  capable  of  being  excited  and  communicated  in  the 
manner  that  heat  is  communicated  in  these  experiments,  except  it 
be  motion." 

Sir  Humphry  Davy  in  1799  showed  that  two  pieces  of  ice 
could  be  melted  by  rubbing  them  together  in  vacuo  at  a  tempera- 
ture of  0°  C.,  and  he  concluded  that  "  Heat  is  motion,  and  its  laws 
of  communication  are  the  same  as  those  of  the  communication  of 
motion." 

The  energy  expended  in  compressing  the  air  in  a  fire-syringe 
may  be  made  to  develop  heat  enough  to  inflame  the  vapor  of  carbon 
bisulphide  and  produce  light.  To  accomplish  this  a  piece  of  cotton 
may  be  moistened  with  carbon  bisulphide  and  placed  at  the  bottom 
of  the  syringe  (Fig.  39) ;  the  piston  may  then  be  inserted,  and  if 
suddenly  shoved  down  a  flash  of  light  will  be  visible. 

The  evident  production  of  heat  in  the  above  case  was  formerly 
accounted  for  by  supposing  that  the  capacity  of  the  gas  for  heat 
was  diminished  by  pressure,  and  that  the  heat  which  it  contained 
was  thus  enabled  to  raise  it  to  a  higher  temperature,  the  pressure 
thus  serving  to  squeeze  out  the  caloric,  and  hence  a  development 
of  heat.  The  same  idea  was  appealed  to  for  an  explanation  of 
the  development  of  heat  in  a  piece  of  soft  iron,  when  rapidly 
pounded  while  resting  upon  an  anvil.  These  explanations  were 
based  upon  the  belief  that  heat  was  a  material  substance,  and  i* 

*  A  mixture  of  water  and  alcohol  will  accomplish  the  result  with  less  work. 


96 


ELEMENTARY  LESSORS 


HEAT. 


was  held  that  these  and  all  similar  phenomena  could  be  explained 
as  depending  upon  altered  distribution  without  any  production  of 
heat. 

Kumford,  in  the  experiments  above  given,  attempted  to  show 

that  this  explanation  was  in- 
sufficient, by  proving  that  the 
metal  shavings  from  the  bored 
gun  had  the  same  capacity  for 
heat  as  the  metal  in  bulk.  Had 
he  shown  this  conclusively,  his 
experiments  would  have  been 
fatal  to  the  material  view  of 
heat ;  but,  although  he  showed 
that  the  heat  developed  was 
out  of  all  proportion  to  what 
might  be  expected  by  such 
view,  he  failed  to  consider  that 
his  metal  chips  were  in  a  dif- 
ferent physical  condition  from 
the  metal  of  the  gun,  and,  for 
his  experiments  to  have  been 
conclusive,  they  should  have 
been  the  same. 

Davy  '  s  experiments,  as 
above  given,  were  entirely  con- . 
elusive  as  to  the  immateriality 
of  heat,  but,  like  Rumford, 
his  failure  to  consider  that  the  ice  and  water  produced  were  in 
different  physical  conditions  made  his  reasoning  less  conclusive. 
Rumfordwas  so  impressed  with  the  idea  that  heat  was  not  material 
that  besought  to  determine  the  ratio  of  heat  to  the  work  necessary 
to  develop  it.  Notwithstanding  these  suggestive  experiments  of 
Rumford  and  Davy,  the  material  view  of  heat  was  almost  universally 
entertained  until  about  1840. 

The  idea  that  heat  and  mechanical  energy  are  definitely  con- 
vertible seems  to  have  been  entertained  by  a  number  of  men  at 
about  this  time.  Seguin  in  France  in  1839,  Mayer  in  Germany  in 
1842,  Colding  in  Denmark  in  1843,  and  Joule  in  England  in  1843  to 
1849  made  and  published  determinations  of  the  mechanical  equiva- 


Fio.  39.— FIRE-SYRINGE. 


THERMO-D  YNAMICS.  97 

lent  of  heat.  So  far  as  the  others  were  •oncerned,  each  of  these 
philosophers  may  be  said  to  have  been  independent  and  original  in 
the  investigations  here  referred  to. 

To  Joule,  however,  must  be  given  the  credit  of  having  first  estab- 
lished exact  numerical  quantitative  relations  between  mechanical 
Energy  and  heat,  thereby  causing  the  general  acceptance  of  the 
aechauical  theory  of  heat. 

Mechanical  Equivalent  of  a  Unit  of  Heat. — The  unit  of  heat  has 
been  already  defined  (p.  27),  and  to  determine  the  amount  of 
energy  necessary  to  be  expended  in  producing  this  heat  was  the 
object  of  Joule's  experiments.  Joule's  method  of  experiment  was 
to  cause  the  mechanical  energy  of  a  descending  weight  to  produce 
friction  between  iron  plates,  or  to  agitate  different  liquids  (water  and 
mercury)  by  means  of  a  paddle-wheel.  In  the  first  case,  of  friction 
between  iron  plates,  the  plates  were  enclosed  in  a  cast-iron  vessel 
filled  with  mercury.  The  heat  developed  was  measured  by  the  rise 
of  temperature  in  the  liquid  agitated,  and,  in  the  case  of  the  iron 
plates,  by  the  rise  in  the  surrounding  mercury.  The  weight  was 
allowed  to  descend  many  times  and  the  mechanical  work  thus  ex- 
pended accurately  computed.  As  accurate  corrections  as  possible 
were  made  for  all  losses  of  heat  by  radiation,  conduction,  rigidity  of 
cords,  and  friction  outside  the  calorimeter,  etc.  The  thermometers 
were  capable  of  indicating  variations  of  ^fa  of  one  degree  F. 

The  conclusions  of  Joule  were  : 

1.  That  the  quantity  of  heat  produced  by  the  friction  of  bodies, 
solids  or  liquids,  is  proportional  to  the  force  expended.* 

2.  That  the  quantity  of  heat  necessary  to  raise  the  temperature 
of  1  pound  of  water  (weighed  in  vacuo  between  55°  and  60°  F.) 
1°  F.,  requires  for  its  evolution  the  expenditure  of  the  mechanical 
energy  represented  by  the  fall  of  772  pounds  through  a  distance  of 
1  foot. 

These  experiments  were  made  at  Manchester,  England,  and 
although  the  foot-pound  does  not  denote  exactly  the  same  energy 
at  all  points  of  the  earth's  surface,  the  variation  is  not  greater 
than  the  probable  error  of  the  determination  ;  we  may  therefore 
say  that  the  energy  comprised  in  one  pound-degree  Fahrenheit 

*  We  should  now  say  energy  expended. 


98  ELEMENTARY  LESSONS  IN  HEAT. 

Is  772  foot-pounds.  For  a  centigrade  degree  this  number  would 
be  1390. 

If  we  take  for  units  the  kilogramme-degree  C.  for  heat,  and  the 
kilogramme-metre  for  work,  this  number  becomes  424,  since  a  kilo- 
gramme is  2.205  pounds  and  a  metre  3.281  feet.  For  the  gramme- 
degree  0.  and  the  gramme-centimetre  it  is  42,400. 

These  numbers  are  known  as  Joule's  Equivalents  in  the  respec- 
tive systems.  Joule's  recent  determinations  (1878)  do  not  sensibly 
change  this  number,  and  it  is  probably  correct  to  within  ^fg-  of  its 
own  amount  (Rankine). 

Prof.  Rowland,  of  the  Johns  Hopkins  University,  has  also 
determined  the  mechanical  equivalent  by  using  Joule's  method  of 
agitating  water  by  a  paddle-wheel.  The  apparatus  devised  by  Prof. 
Rowland  could  hardly  be  surpassed  in  the  perfection  of  arrange- 
ment necessary  to  accurate  results.  The  advantages  of  Rowland's 
arrangement  as  compared  with  Joule's  can  only  be  fully  appreciated 
from  a  full  description,  such  as  cannot  be  here  given.  The  mean 
difference  between  Rowland's  and  Joule's  determinations,  when  the 
latter's  temperatures  were  reduced  to  those  of  the  air  thermometer, 
amounts  to  only  1  in  430.  Prof.  Rowland's  determinations  showed 
conclusively  that  the  specific  heat  of  water  decreased  with  an  in- 
crease of  temperature,  and  his  value  for  the  mechanical  equivalent 
of  a  unit  of  heat  when  water  is  taken  at  the  temperature  of  60°  F. 
is  778.9.  Prof.  Rowland  thinks  that  subsequent  experiments  will 
not  change  his  results  more  than  1  in  500.  At  15.5°,  the  equivalent 
temperature  on  the  centigrade  scale,  the  number  is  1402. 

There  are  other  methods  for  determining  the  mechanical  equiva- 
lent, and  the  agreement  of  all  the  results  is  now  deemed  conclusive 
that  equal  quantities  of  mechanical  energy  always  correspond  to 
the  same  amount  of  heat. 

The  measurement  of  the  work  done  by  heat,  or  the  inverse  of 
Joule's  problem,  was  first  accomplished  by  Hirn  in  1862.  His 
results,  when  the  mechanical  difficulties  of  the  problem  are  con- 
sidered, are  completely  confirmatory  of  Joule's. 

When  heat  is  measured  as  a  quantity,  it  should  be  remembered 
that  the  temperature  or  condition  of  the  body  in  which  it  exists  is 
immaterial.  The  mechanical  equivalent  of  a  definite  amount  of 
heat  is  always  the  same,  no  matter  what  tho  temperature  of  the 


THERMO-DTNAMIC8.  99 

body  in  which  it  exists.     The  heat,  however,  is  more  available  for 
conversion  into  mechanical  energy  when  at  a  high  temperature. 

First  Law  of  Thermo-Dynamics. — A  correct  expression  for  the 
relation  between  heat  and  mechanical  energy  constitutes  the  First 
Law  of  Thermo-dynamics.  It  is  expressed  by  the  equation  W  =  JH, 
in  which  W  denotes  work,  J  Joule's  equivalent,  and  H  heat  units. 

When  heat  is  admitted  to  be  a  form  of  energy  and  the  theory  of 
the  conservation  of  energy  is  accepted,  the  truth  involved  in  the 
above  expression  is  axiomatic,  and  it  is  but  a  particular  case  of 
transmutation  of  energy.  Work  is  not  energy,  but  rather  the 
operation  or  process  by  which  energy  is  transmuted.  The  amount 
of  work  is  measured  by  the  energy  transmuted,  which  is  always  left 
behind  in  some  other  form. 

This  transmutation  of  heat  into  mechanical  energy  and  of 
mechanical  energy  into  heat  is  so  familiar  that  it  barely  needs 
to  be  referred  to.  All  steam-boats,  cars,  steam-pumps,  power  en- 
gines, etc.,  derive  their  useful  motion  and  work  from  the  heat 
energy  of  the  burning  coal  in  their  furnaces.  In  these  same  cases 
we  find  the  energy  of  the  moving  parts  by  friction  and  concussions 
producing  heat. 

Heat  Consumed  in  Expansion. — When  a  gas  expands  without 
having  to  overcome  external  resistance,  that  is,  without  doing 
external  work,  its  temperature  is  not  sensibly  changed  ;  but  when 
it  does  external  work  its  temperature  falls.  A  gas  which  develops 
mechanical  power  in  expanding  can  only  be  kept  at  a  constant 
temperature  by  the  addition  of  heat  to  it,  and  the  heat  necessary  to 
be  thus  added  is  nearly,  though  not  exactly,  the  thermal  equivalent 
of  the  work  done  by  the  gas  during  expansion;  the  approach  to 
equality  being  the  nearer,  the  nearer  the  gas  approaches  the  condi- 
tion of  a  perfect  gas.  Consequently,  if  a  gas  does  work  without 
transfer  of  heat  to  or  from  it,  the  thermal  equivalent  of  the  work 
must  disappear  as  heat.  It  is  thus  evident  why  it  was  necessary  to 
make  a  distinction  between  the  specific  heat  of  a  gas  at  constant 
volume  and  at  constant  pressure.  The  work  done  by  a  gas  on  ex- 
panding against  uniform  hydrostatic  or  pneumatic  pressure  may  be 
computed  by  multiplying  the  increase  of  rolnme  b?  th^  pressure 
per  unit  of  area. 


100  ELEMENTARY  LESSONS  IN  HEAT. 

Thermic  Engines. — In  all  forms  of  thermic  engines  work  is 
obtained  by  means  of  expansion  produced  by  heat  in  some  elastic 
fluid,  the  expansive  force  usually  acting  on  a  piston  travelling  in  a 
cylinder.  Of  the  heat  received  from  the  source  by  the  fluid  a  frac- 
tion only  can  under  any  circumstances  be  converted  into  mechanical 
work.  A  portion  is  lost  by  conduction  through  the  parts  of  the 
apparatus,  another  portion  remains  in  the  fluid  when  it  escapes  into 
the  air  or  condenser,  and  a  third  portion  has  disappeared  and  ceased 
to  exist,  for  the  time  being,  as  heat.  The  heat  thus  converted  or 
utilized  bears  to  that  received  from  the  source  a  simple  relation  de- 
pending only  upon  the  temperatures  of  the  source  and  refrigerator. 
The  second  law  of  thermo-dynamics  refers  to  this  relation,  and  one 
of  its  expressions  may  be  made  in  this  form :  No  part  of  the  heat  of 
a  material  object  by  the  action  of  natural  processes  alone  can  be  con- 
verted into  mechanical  energy  except  by  allowing  the  other  part  to 
pass  from  that  body  into  other  bodies  at  a  lower  temperature. 

In  the  conversion  of  heat  into  mechanical  energy  by  engines,  or 
doing  work  by  means  of  heat,  the  expanding  fluid  (as  air  in  the 
hot-air  engine,  or  steam  in  the  steam-engine)  is  called  the  working 
substance.  In  order  that  the  process  may  be  continuous,  it  is  evi- 
dent that  the  action  of  the  machine  by  which  the  conversion  is  ac- 
complished must  be  periodic  ;  that  is  to  say,  after  a  series  of  changes 
all  parts  of  the  machine  must  return  to  the  same  relative  positions 
and  conditions  as  at  the  beginning  ;  and  to  facilitate  the  conception 
here  desired,  the  condition  of  the  working  substance  at  the  end  of 
the  operation  will  be  taken  the  same  as  at  the  beginning.  A  series 
of  operations  by  which  this  result  is  accomplished  is  called  a  cycle. 
If  the  working  substance  is  not  in  exactly  the  same  condition  at  the 
end  of  the  cycle  as  at  the  beginning,  we  should  have  to  know  the 
energy  involved  in  the  change  of  condition  before  we  could  estimate 
the  other  work  involved  in  the  cycle. 

To  determine  the  law  governing  the  performance  of  work  by 
the  conversion  of  heat  into  mechanical  energy,  recourse  is  had  to 
a  conception  of  Sadi  Carnot  set  forth  in  1824,  and  brought  into 
renewed  prominence  by  Prof,  (now  Sir  William)  Thomson  in  1848. 
Carnot's  machine  is  an  entirely  imaginary  one  and  impossible  of 
construction,  and  used  only  for  scientific  illustration  and  deduction  ; 
but  by  describing  an  ideally  perfect  engine  he  brings  out  the  points 


THERMO-D  YNAMICS. 


W 


to  be  kept  in  view  in  the  construction  of  possible  engines  in  any  case. 
This  ideal  engine  is  usually  known  as  Carnot's  reversible  engine. 

Carnot's  Cycle. — The  conception  is  as  follows  : 

Suppose  we  have  a  cylinder,  with  piston  P  (Fig.  40),  containing 
air  as  the  working  substance,  though  we  might  take  any  other.  The 
walls  of  the  cylinder  and  the  piston  are  absolute  non-conductors  and 
non-absorbers  of  heat,  the  bottom  of  the  cylinder  is  a  perfect  con- 
ductor and  without  specific  heat ;  heat  to  and  from  the  cylinder 
can  only  pass  through  this  bottom.  Wis  a  body  which  is  a  perfect 
non-conductor  and  non- 
absorber  of  heat,  H  and 
L  are  bodies  at  tempera- 
tures which  remain  con-  - 
stant  during  the  opera- 
tion, that  of  H  being  — 
higher  than  that  of  L. 

Let  us  suppose  that  ~ 
the  cylinder  stands  on 
TFand  the  piston  is  any 
distance  above  the  bot- 
tom, and  the  working 
substance  (which  we 
will  hereafter  for  brev- 
ity indicate  by  ws)  at 
the  temperature  of  L. 

1st  Operation. — Let 
the  piston  be  depressed 
until  the  temperature  of 
ws  rises  to  that  of  H. 

2d  Operation. — Now  transfer  the  cylinder  to  the  hot  body  H, 
and  allow  the  piston  to  rise  :  the  expansion  of  ws  tends  to  produce  a 
fall  of  temperature  ;  but  this  is  prevented  by  heat  flowing  in  through 
the  perfectly  conducting  bottom  of  the  cylinder,  and  ws  expands  at 
the  temperature  of  H  and  the  piston  ascends  through  a  certain 
distance. 

3d  Operation. — Now  move  the  cylinder  back  to  W  and  allow 
the  piston  to  rise,  and  let  ws  expand  until  its  temperature  falls  to 
that  of  L,  then  stop  the  expansion. 


OA'     of          B'       C' 

FIG.  41.— GEOMETRICAL  ILLUSTRATION. 


- 


*1G2  "ELEMENTARY  LESSONS  IN  HEAT. 

4th  Operation. — Now  transfer  the  cylinder  to  the  colder  body  L 
and  depress  the  piston.  The  temperature  of  ws  would  rise,  but  it 
is  prevented  by  the  heat  flowing  through  the  bottom  of  the  cylinder 
into  L.  When  the  piston  is  depressed  to  the  point  at  which  we 
commenced  in  the  first  operation,  let  the  cylinder  be  transferred  to 
W.  Everything  will  now  be  exactly  as  it  was  in  the  beginning,  and, 
with  the  imagined  arrangement,  the  operation  can  be  repeated  in- 
definitely, a  cycle  being  completed  each  time  these  operations  are 
gone  through  with. 

Work  done  during  the  Cycle. — During  the  cycle  there  were 
two  elevations  and  two  depressions  of  the  piston.  During  the  ele- 
vations work  was  done  by  ws  (working  substance),  measured  by  the 
average  pressure  on  unit  of  area  in  each  case  multiplied  by  the 
distance  through  which  the  piston  moved ;  during  the  depressions 
work  was  done  upon  ws,  measured  in  each  case  in  the  same  wav 
Since  the  piston  at  the  end  of  the  cycle  is  in  the  same  position  as  at 
the  beginning,  the  sums  of  the  elevations  must  be  equal  to  the  sums 
of  the  depressions :  and  since  the  elevations  took  place  at  the  higher 
temperature,  the  average  pressures  during  the  elevations  must  have 
been  greater;  therefore,  the  work  done  by  ws  during  the  elevations 
must  have  been  greater  than  that  done  upon  it  during  the  depres- 
sions. As  these  operations  can  be  continued  indefinitely,  we  have 
a  means  of  obtaining  useful  work. 

Transference  of  Heat  during  Cycle.  —  From  the  conditions 
imposed  upon  our  ideal  engine,  it  will  be  seen  that  there  was  no 
transference  of  heat  to  or  from  the  cylinder,  except  during  the 
second  and  fourth  operations.  During  the  second  operation  heat 
was  taken  from  the  hot  body,  and  during  the  fourth  heat  was  given 
to  the  cold  body. 

Results  and  Conclusions. — At  the  end  of  the  cycle  everything  is, 
so  far  as  we  are  able  to  discover,  exactly  as  at  the  commencement; 
more  work  has  been  done  by  the  substance  than  upon  it,  and  a  cer- 
tain quantity  of  heat  has  been  taken  from  the  hotter  body  and  a  cer- 
tain quantity  transferred  to  the  colder  body.  The  principle  of  the 
conservation  of  energy,  which  cannot  be  shaken  by  any  evidence 
yet  available  to  us,  teaches  that  the  useful  work  (the  excess  of  work 


THERMO-DYNAMICS.  103 

done  by  over  that  done  upon  ws)  must  arise  from  some  expenditure 
of  energy.  With  our  present  knowledge  the  only  conceivable 
source  is  the  heat  taken  in  during  the  second  operation,  and  there- 
fore we  conclude  that  the  heat  taken  in  during  the  second  operation 
is  greater  than  that  given  out  during  the  fourth  by  an  amount 
equivalent  to  the  useful  energy.* 

If  W  represent  the  useful  energy  obtainable  from  the  engine, 

W 
and  Q  the  heat  communicated  to  it  at  the  higher  temperature,  -~ 

measures  the  efficiency  of  the  engine;  or  if  Q'  equal  the  heat  given 
out  by  ws  at  the  end  of  the  operation,  the  efficiency  may  be  written 

Q-Q' 
Q    ' 

or  the  efficiency  of  the  engine  may  be  defined  as  the  ratio  of  the  heat 
converted  into  work  to  the  whole  amount  which  enters  the  engine.  . 

Geometrical  Illustration. — The  above  cycle  of  operations  may 
be  illustrated  geometrically  as  follows  :f  In  our  cylinder  the  dis- 
tance between  the  piston  and  the  bottom  of  the  cylinder  is  always 
proportional  to  the  volume  of  the  working  substance;  now  let,  in 
the  diagram  (Fig.  41,  p.  101),  A',  B',  C' ',  and  D'  be  the  positions  of 
the  piston  at  the  end  of  each  operation,  and  0  the  bottom  of  the 
cylinder,  and  let  AA',  BB',  CC',  and  DD'  be  perpendiculars  pro- 
portional to  the  pressures  at  these  points. 

At  the  end  of  the  fourth  operation  and  at  the  beginning  of  the 
first,  the  piston  is  at  D'.  During  the  first  operation  the  volume  is 
decreased  and  the  pressure  increased,  the  piston  moving  to  A'.  The 
work  done  during  the  compression  is  equal  to  the  mean  pressure 

*  Carnot  thought  that  the  useful  energy  was  due  to  the  loss  of  temperature 
by  the  heat.  He  thought  that  the  energy  of  a  given  quantity  of  heat  was 
greater  when  it  existed  in  a  hot  body  than  when  in  a  cold  one.  We  now  know 
that  the  mechanical  energy  of  a  given  quantity  of  heat  is  the  same,  no  matter 
at  what  temperature  it  exists. 

f  The  diagram  is  known  as  the  "  indicator  diagram,"  and  is  very  conven- 
ient for  representing  and  explaining  to  the  eye  the  working  of  a  fluid  of 
variable  volume.  It  is  not  deemed  necessary  here  to  fully  describe  the  princi- 
ples of  this  method  of  indicating  the  working  of  a  fluid.  The  statements 
referred  to  in  connection  with  the  diagram  are  susceptible  of  easy  proof. 


104  ELEMENTARY  LESSONS  IN  HEAT. 

exerted  on  the  piston  multiplied  by  the  distance  A'D'.  The  mean 
pressure  is  somewhere  between  A  and  D>  and  the  pr  xluct  is  the 
area  AA'D'D\  the  work  is  proportional  to  the  area  and  may  be 
represented  by  it.  In  the  same  way  it  follows  that  the  work  in  the 
2d,  3d,  and  4th  operations  maybe  represented  by  the  areas  //ABB', 
B'BCC',  and  C'CDD',  respectively. 

The  work  done  by  ws  during  the  whole  expansion  is  represented 
by  the  area  A'ABCC',  that  done  upon  ws  during  compression  is 
represented  by  the  area  A' AD  CO',  and  the  difference  or  balance 
of  useful  work  is  represented  by  the  area  ABCD.  It  is  likewise 
provable  that  the  area  A' ABB'  described  under  the  circumstances 
is  proportional  to  the  heat  imparted  to  ws  during  the  2d  operation, 
and  the  area  D'DCC'  is  proportional  to  the  heat  given  out  by  ws 
during  the  4th  operation,  and  that  heat  has  disappeared  represented 
by  the  area  ABCD,  which  is  the  representation  of  the  work  done  j 
the  ratio 

ABCD 
A' ABB' 

on  the  diagram  represents  the  efficiency  of  the  engine. 

Principle  of  Reversibility.— This  hypothetical  engine  of 
Carnot's  is  also  reversible, — that  is  to  say,  all  the  operations  de- 
scribed may  be  performed  in  the  reverse  order,  as  follows : 

Referring  to  Fig.  41,  let  us  begin  at  the  temperature  of  the 
colder  body  L  and  volume  OD'  (on  diagram),  let  the  cylinder  be 
placed  on  L  and  allow  expansion  from  volume  OD'  to  OC' ';  ^vs 
(working  substance)  will  receive  from  L  a  quantity  of  heat.  Let 
the  cylinder  then  be  transferred  to  W  and  the  piston  compressed 
until  the  volume  is  OB' ;  ws  would  then  have  the  temperature  of 
H.  Now  transfer  the  cylinder  to  IT  and  press  the  piston  to  volume 
OA' ;  during  this  operation  ws  will  give  out  a  quantity  of  heat  to 
H.  Lastly,  transfer  the  cylinder  to  PFand  let  expansion  occur  to 
OD'\  ws  will  then  be  in  its  original  state.  Now,  by  considering 
the  diagram,  and  remembering  that  the  areas  marked  out  are  pro- 
portional to  the  work  done  during  the  motion  of  the  piston  and 
also  to  the  transfers  of  heat  during  the  1st  and  3d  operations,  it  is 
seen  that  more  work  is  done  upon  ws  than  by  it,  and  that  more 
is  communicated  to  H  than  was  taken  from  L.  The  same 


THERMO-DYNAMICS.  105 

fact  is  evident  when  we  consider  that  the  work  done  upon  ws  is 
during  the  compression  of  the  piston,  and  that  by  it  during  the 
elevation,  and  that  the  former  takes  place  at  the  higher  temper- 
ature. 

With  such  an  engine  we  see  that  it  is  possible  to  transfer  heat 
from  a  body  at  a  lower  to  one  at  a  higher  temperature,  but  that 
such  result  can  only  be  accomplished  by  the  expenditure  of  me- 
chanical energy.  If  we  accept  this  as  the  only  means  of  such 
transfer  (and  our  experience  compels  us  to  deny  every  other),  it 
can  be  readily  shown  that  the  efficiency  of  a.  reversible  engine  is 
the  greatest  that  can  be  obtained  with  a  given  range  of  tempera- 
ture.* ISo  engine,  therefore,  could  be  more  perfect  than  a  reversi- 
ble one;  hence,  reversible  engines  being  perfect,  they  all  convert 
the  same  proportion  of  the  heat  received  into  mechanical  energy 
when  working  between  the  same  temperatures  of  source  and  re- 
frigerator, no  matter  what  the  working  substance  be.  It  can  be 
further  shown,  from  the  principles  of  the  indicator  diagram,  that 
the  quantity  of  work  can  only  be  increased  by  increasing  the 
quantity  of  heat  taken  in,  or  with  the  same  quantity  of  heat  by 
increasing  the  difference  between  the  temperatures  of  the  hotter 
and  colder  bodies  which  diminishes  the  amount  given  out. 

Absolute  Temperatures. — The  conceptions  of  Carnot,  as  Sir 
W.  Thomson  f  has  pointed  out,  give  also  the  conception  of  a  scale 
of  temperatures  the  definition  of  which  is  independent  of  the 
nature  of  any  particular  substance.  From  the  above  principles  it 
is  seen  that  quantities  of  heat  and  intervals  of  temperature  are  the 
only  elements  upon  which  the  useful  work  of  a  perfect  engine 
depends,  arid,  if  the  quantity  of  heat  taken  in  by  the  working 
substance  be  constant,  the  useful  work  depends  only  upon  inter- 
vals of  temperature  between  the  source  and  refrigerator.  If  the 
intervals  of  temperature  in  different  cases  then  be  so  divided  that 
the  number  of  divisions  is  proportional  to  the  quantities  of  heat 
converted  into  useful  work,  then  these  divisions  will  be  as  definite 
and  absolute  as  are  our  measurements  of  quantities  of  heat. 

On  a  scale  with  such  divisions  or  degrees  the  numbers  of  de- 
grees between  different  intervals  would  be  proportional  to  the 

*  See  foot-note  on  page  1 19 

f  Cambridge,  P.  8.  P.,  June,  1848. 


J06  ELEMENTAET  LESSONS  IN  HEAT. 

amounts  of  useful  work  done  by  a  perfect  engine  when  working 
through  these  intervals  and  taking  in  the  same  quantity  of  heat 
each  time.  Now,  if  the  temperature  of  the  hotter  body  be  fixed 
and  the  quantity  of  heat  taken  in  be  fixed,  the  useful  work  done 
depends  only  on  the  temperature  of  the  lower  body  or  refrigerator. 
If  the  temperature  of  the  refrigerator  be  so  determined  that  the 
useful  work  done  shall  be  equal  to  the  total  heat  received,  we  could 
not  possibly  have  more  work  than  this  from  that  amount  of  heat ; 
consequently  such  a  point  would  be  the  absolute  zero,  and  we 
would  be  precluded  from  a  negative  temperature  on  such  a  scale. 
In  terms  of  such  a  scale  as  just  described  the  efficiency  of  a 

T—  Tf 

perfect  engine  can  be  shown  to  be  equal  to  — ~ — 9  or 

Q-  Q'  _  T-  T' 

Q  '  T 

in  which  Q  is  the  quantity  of  heat  taken  in,  Q'  the  quantity  given 
out,  and  T  and  T'  the  absolute  temperatures  of  the  source  and 
refrigerator  respectively.  From  the  above  we  have 

«-£'. 
T  ~  T" 

or,  absolute  temperatures  may  be  defined  as  such  as  are  propor- 
tional to  the  quantities  of  heat  taken  in  and  given  out  by  perfect 
engines. 

From  the  above  considerations  it  is  seen  that  in  order  to  con- 
struct a  scale  of  absolute  temperatures  it  is  only  necessary  to  deter- 
mine the  maximum  amount  of  mechanical  energy  that  a  given 
quantity  of  heat  (say  one  unit)  is  capable  of  giving  out  during  its 
transmission  from  a  body  at  one  temperature  to  another  at  a  lower 
temperature;  that  is,  the  same  amount  as  would  be  given  out  by  a 
perfect  engine  between  these  temperatures.  The  discussions  of 
Carnof  s  ideal  engine  have  shown  what  physical  properties,  capable 
of  experimental  determination  in  certain  working  substances,  are 
necessary  to  obtain  this  amount  of  work.*  By  taking  the  number 

*  The  experiments  necessary  to  be  made  on  the  working  substance  for  the 
determinations  of  the  quantities  of  heat  taken  in  and  given  out  by  a  perfect 
engine  have  not  been  successfully  made,  but  in  a  different  way  the  absolute 
dynamical  scale  has  been  compared  with  the  so-called  absolute  scale  of  the  air 
thermometer..  (See  Maxwell's  Theory  of  Heat.) 


TIIERMO-DYNAMICS.  107 

of  degrees  between  the  temperatures  considered  the  same  as  that 
by  any  of  our  ordinary  scales,  it  is  evident  that  the  size  of  our 
absolute  degrees  will  be  equal  to  the  mean  value  of  the  degree  on 
the  scale  used.  The  comparison  of  the  absolute  thermo-dynamic 
scale  with  that  of  the  air  thermometer  shows  them  to  be  almost 
exactly  the  same,  the  absolute  zero  on  the  two  scales  is  within  a 
fraction  of  a  degree  centigrade  of  the  same  point,  when  the  abso- 
lute thermo-dynamic  degrees  are  so  taken  as  to  make  100  between 
the  freezing  and  boiling  temperatures  of  water. 

In  concluding  this  discussion  of  Carnot's  cycle,  it  may  be  well 
to  add  that  in  practice  the  cycle  is  not  usually  completed,  the 
same  portion  of  the  working  substance  not  being  made  repeatedly 
serviceable.  At  a  certain  point  of  its  expansion  the  working  sub- 
stance may  be  discharged  into  the  atmosphere  and  a  fresh  portion 
taken  in  to  supply  its  place.  In  the  case  of  steam,  when  a  con- 
denser is  used,  the  water  produced  is  returned  to  the  boiler,  but 
here  the  regularity  of  the  cycle  is  broken  by  the  abrupt  condensa- 
tion of  the  steam  before  it  has  done  all  the  work  of  which  it  is 
capable.  In  general  a  portion  of  the  useful  work  in  engines  has  to 
be  sacrificed  to  avoid  a  greater  loss  in  establishing  a  complete  cycle. 
Besides  this  loss  of  useful  work  there  is  loss  of  heat  at  every  stage 
of  the  operation  by  radiation  and  conduction.  But,  discarding 
these  sources  of  loss  and  assuming  a  perfect  engine,  it  will  be  seen 
from  the  expression  for  the  efficiency 


that  only  a  small  fraction  of  the  heat  taken  in  is  converted  into 
mechanical  energy;  for,  suppose  we  have  an  engine  working  under 
a  pressure  of  130  pounds  per  square  inch,  this  would  require  a 
temperature  of  185°  C.,  which  reckoned  from  the  absolute  zero 
would  be  458°  for  the  upper  temperature,  and  if  the  engine  be 
non-condensing  the  lower  temperature  would  be  373°  on  the  abso- 
lute scale;  these  numbers  in  the  expression  above  give 

458  -  373  , 

-453— =  0.19  nearly. 


108  ELEMENTARY  LESSONS  IN  HEAT. 

Steam-Engine. — We  shall  now  explain  the  elementary  principles 
of  the  reciprocating  steam-engine  and  describe  the  essential  parts. 

The  earliest  application  of  the  principle  for  accomplishing  use- 
ful work  is  said  to  have  been  made  by  Savery,  an  English  mining 
engineer,  about  1697.  He  invented  a  machine  by  which  the  press- 
ure of  steam  was  made  to  force  water  from  a  receiver  up  through 
an  ascending  pipe,  and  then  by  condensing  the  steam,  by  the  appli- 
cation of  cold  water  to  the  outside  of  the  receiver,  more  water  was 
forced  by  atmospheric  pressure  into  the  receiver  and  the  operation 
repeated.  This  was  really  a  steam-pump,  and  was  to  a  limited 
extent  used  in  draining  mines. 

Papin,  the  inventor  of  the  digester  (page  44)  and  of  the  safety- 
valve,  was  the  first  to  conceive  the  idea  of  making  steam  move  a 
piston  and  thus  communicate  motion  to  mechanism.  He  con- 
structed in  1690  a  working  model  which  consisted  of  a  vertical 
cylinder  with  a  piston  and  a  little  water  beneath  it.  By  converting 
the  water  into  steam  the  piston  was  forced  up,  and  upon  condensa- 
tion of  the  steam  the  atmosphere  forced  the  piston  down.  Papin's 
cylinder  was  also  the  boiler,  and  the  condensation  was  brought 
about  by  removing  the  cylinder  from  the  fire  and  cooling  it. 

Newcomen,  Savery,  and  Cawley,  in  1705,  combined  the  cylinder 
and  piston  with  the  separate  boiler,  and  condensed  the  steam  by 
injection  of  cold  water  into  the  cylinder.  The  descent  of  the 
piston  was  produced  by  the  atmosphere,  and  hence  the  engine  is 
generally  referred  to  as  Newcomen's  atmospheric  engine.* 

In  1763  and  1764  James  Watt,  while  repairing  a  model  of  New- 
comen's  engine  (belonging  to  the  University  of  Glasgow,  and  still 
preserved  there),  perceived  the  defects  of  the  machine,  and  con- 
ceived the  idea  of  improving  it.  In  1769  his  first  patents  were 
taken  out.  His  first  improvement  consisted  in  the  introduction 
of  a  separate  vessel  for  the  condensation  of  the  steam.  In  the 
second  improvement  he  substituted  the  pressure  of  steam  for 
the  atmospheric  pressure  which  caused  the  downward  stroke  in 
Newcomen's  engine ;  the  upward  stroke  was  effected  by  means  of  a 
counterpoise,  the  steam  pressing  equallv  on  the  two  sides  of  the 

*  Arrangements  for  automatically  operating  the  valves  of  an  engine  were 
devised  by  Newcomen  and  Savery  and  are  shown  in  a  cut  of  an  engine  erected 
by  them  in  1712.  Desaguliers  in  his  Experimental  Philosophy,  vol.  n,  1743, 
claims  this  improvement  for  a  boy,  Humphrey  Potter,  1713,  but  the  above  fact 
disproves  the  claim. 


THERMO  D  YNAMICS. 


109 


piston.  This  engine  succeeded  Newcomen's,  and  is  known  as  the 
Single-Acting  Engine,  because  only  the  down-stroke  is  produced  by 
the  steam.  It  is  still  frequently  employed,  because  of  the  sim- 
plicity of  its  arrangements.  It  was  not  long  before  Watt  perfected 
his  engine  by  employing  steam  to  produce  both  strokes.  This  is 
the  characteristic  of  the  DouUe-Acting  Engine,  and  the  improve- 
ments since  Watt's  time  have  been  of  detail  rather  than  principle. 
Early  attempts  at  steam  navigation  had  been  made  before,  but  it 
was  first  established  on  a  commercial  basis  in  1807  by  Fulton  on  the 
Hudson  River,  New  York.  Fulton's  vessel  was  driven  by  an  engine 
made  by  Boulton  and  Watt, 

Double- Acting  Engine. — The  principle  of  this  engine  is  very 
simple,  and  will  be  understood  from  the  figure  (Fig.  42).     The 


FIG.  42.— DOUBLE- 
ACTING  ENGINE. 


FIG.  43.— PISTON  CONNECTIONS. 


steam  is  admitted  from  the  boiler  to  the  top  and  bottom  of  the 
cylinder  by  the  pipes  a  and  b,  and  escapes  from  the  cylinder  to  the 
condenser  through  the  pipes  c  and  d.  If  the  stopcocks  a  and  d  are 
open  while  b  and  c  are  closed,  it  is  evident  that  the  steam  from  the 
boiler  will  force  the  piston  in  one  direction;  and  then,  if  a  and  d  be 
closed  and  b  and  c  be  open,  the  piston  will  be  driven  in  the  other 
direction.  By  suitable  connections  with  the  rod  of  the  piston,  this 
alternate  motion  can  be  converted  into  one  of  rotation. 

The  principle  by  which  this  rectilinear  motion  of  the  piston  is 
converted  into  circular  motion  is  shown  in  the  diagram  (Fig.  43),  in 
which  D  is  the  cylinder,  P  the  piston,  r  the  piston-rod,  r'  the  con- 


110 


ELEMENTARY  LESSONS  IN  HEAT. 


necting-rod,  and  r"  the  crank.  It  will  be  seen  from  the  figure  that 
at  the  beginning  and  end  of  the  stroke  in  this  arrangement  the 
piston-rod,  connecting-rod,  and  crank  are  in  the  same  right  line, 
and  pressure  on  the  piston  at  these  positions  will  not  turn  the  crank 
either  way.  These  positions  of  the  piston  are  called  the  dead 
points.  The  momentum  of  the  wheel  or  machinery  to  which  the 
crank  communicates  motion  carries  it  beyond  these  points,  and  the 
motion  is  continued. 

Arrangements  for  Admitting  Steam. — In  the  above  simple  de- 
scription we  have  supposed  the  cocks  to  be  operated  by  hand,  but 
the  opening  and  closing  of  steam-passages  is  really  effected  auto- 
matically, and  the  distribution  of  steam  is  regulated  by  valves. 
The  arrangement  of  the  simplest  form  of  slide-valve  is  shown  in 
the  figures  (Figs.  44  and  45).  The  steam,  instead  of  entering  the 
cylinder  direct,  first  passes  into  the  steam-chest  C.  Besides  the 
opening  for  the  admission  of  steam  in  the  chest,  not  shown  in  the 


FIG.  44.— SLIDE-VALVE  CENTRAL. 


FIG.  45. — SLIDE-VALVE  UPWARD. 


figure,  there  are  three  other  holes  called  ports  ;  two  of  these,  a  and 
«',  communicate  with  the  cylinder  at  the  opposite  ends,  and  the 
other,  Hy  communicates  with  the  condenser.  D  is  the  slide-valve, 
and  in  this  case  is  exactly  the  length  contained  between  the  outer 
edges  of  the  steam-ports,  and  its  faces  are  just  sufficient  to  cover  the 
widths  of  the  steam-ports.  In  Fig.  45,  when  the  valve  is  at  the  up- 
ward part  of  its  stroke,  the  steam  is  admitted  to  the  lower  part  of 
the  cylinder  from  the  chest  and  escapes  into  the  condenser  from  the 
upper  part  through  the  port  a'  and  H\  the  reverse  is  the  case  when 


TEERMO-DYNAMWS.  Ill 

the  ^alve  is  down.     The  slide-valve  is  moved  automatically  by  the 

engine  itself  by  means  of  an  eccentric  or  other  arrangement. 

An  eccentric  is  a  species  of  crank.  A  simple  form  consists  of  a 
circular  piece  of  metal  e  (Fig.  46),  called  the  eccentric.  This  is 
traversed  by  the  shaft  of  the  engine  in  a  point  other  than  the 
centre.  The  eccentric  is  firmly  attached  to  and  revolves  with  the 
shaft.  This  eccen- 
tric turns  inside  a 
ring  of  metal,  which 
ring  is  rigidly  con- 
nected to  the  frame- 
rod  T.  It  is  evident  FlG"  46-S'™ 

that  the  rotation  of  the  shaft  will  cause  a  reciprocating  motion  in 
T,  which  by  suitable  gearing  can  be  made  to  move  the  valve.  The 
distance  from  the  centre  of  the  eccentric  to  the  centre  of  the  shaft 
is  called  the  eccentric  radius. 

The  simple  D-valve  just  described,  for  illustrating  the  principle 
of  valves,  is  in  common  use  in  the  smaller  types  of  land  engines  and 
locomotives,  but  there  are  many  other  forms  and  arrangements  of 
valves  more  advantageous  in  larger  engines. 

The  double-ported  slide-valve,  the  piston-valve,  and  the  cylindri- 
cal valves  of  the  Corliss  engine  are  examples  of  these,  but  their  de- 
scription is  not  appropriate  to  this  book. 

Modification  of  D-Valve  for  Expansive  Working. — By  the  simple 
valve  just  described,  and  when  the  radius  of  the  eccentric  is  at 
right-angles  to  the  crank,  steam  is  admitted  on  one  side  of  the 
piston  during  the  whole  length  of  the  stroke ;  and  the  port  to  the 
condenser,  or  exhaust  on  the  other  side,  is  also  open  during  the 
same  time.  In  such  an  arrangement  steam  of  the  same  density 
and  pressure  acts  on  the  piston  during  the  entire  stroke,  and  steam 
only  begins  to  be  admitted  to  the  cylinder  as  the  valve  moves  from 
its  central  position  (Fig.  44),  and  the  steam  is  completely  exhausted 
from  the  cylinder  on  the  side  of  the  piston  toward  which  motion 
takes  place,  because  the  exhaust  on  that  side  is  open  all  the  while 
the  piston  moves  in  that  direction. 

In  practice  these  features  do  not  exist.  The  steam  is  cut  off 
comparatively  early  in  the  stroke,  and  acts  by  expansion  during 


ELEMENTARY  LESSONS  IN  HEAT. 

the  remainder  of  it;  the  exhaust  is  also  closed  before  the  end  of  the 
stroke,  so  that  the  steam  left  in  the  cylinder  is  compressed  and  acts 
like  a  cushion  before  the  advancing  piston,  and  the  arrangement  is 
such  that  steam  is  admitted  just  before  instead  of  just  after  the  be- 
ginning of  the  stroke. 

These  first  two  objects  are  usually  accomplished  by  increasing 
the  width  of  the  faces  of  the  valve,  as  shown  in  Fig.  47;  the  width 

added  to  the  outside  is  called 
outside  lap,  the  other  the 
inside  lap.  By  such  an  ar- 
rangement the  admission  and 
escape  of  steam  is  cut  off 
earlier  than  with  a  valve 

FIG.  47.— VALVE  FOR  EXPANSIVE  WORKING. 

without  lap,  and  the  expan- 
sive action  of  the  steam  is  secured  on  the  driving  side  of  the  piston 
and  the  cushioning  effect  on  the  other. 

In  working  expansively,  the  part  of  the  stroke  at  which  the  cut- 
off occurs  varies  considerably, — sometimes  at  half-stroke,  sometimes 
at  one-quarter,  and  sometimes  at  one-fifth  of  the  stroke.  The  above 
is  not  the  only  way  of  regulating  the  amount  of  expansion. 

The  amount  by  which  the  admission  steam-port  is  open  at  the 
commencement  of  the  stroke  is  called  the  lead,  and  is  brought 
about  by  the  proper  adjustment  of  the  positions  of  the  crank  and 
the  radius  of  the  eccentric. 

The  above  arrangement  is  usually  sufficient  for  ordinary  en- 
gines which  work  in  one  direction,  but,  where  engines  have  to  be 
frequently  reversed,  other  arrangements  have  to  be  adopted.  The 
method  usually  employed  is  known  as  Stephenson's  link-motion, 
though  there  are  others  in  use.  Without  describing  in  detail  this 
arrangement,  we  may  say  that  it  consists  of  two  eccentrics  op- 
positely placed  on  the  shaft,  and  the  slide-valve  rod  can  be  shifted 
from  one  to  the  other  by  means  of  a  link  and  the  valve  thus  be 
made  to  obey  either  eccentric,  and  this  change  reverses  the  engine. 
When  the  link  is  kept  half-way  between  the  two  eccentrics,  the 
valve  remains  in  its  central  position,  no  steam  is  admitted,  and  the 
engine  stops.  By  varying  the  position  of  the  link,  the  distri  mtion 
of  the  steam  can  be  entirely  modified.  Locomotive  engines  iind 
most  engines  needing  frequent  reversals  are  regulated  in  this  way, 
not  being  fitted  with  governors. 


THERMO-D  YNAMIGS. 


113 


Governors. — To  prevent  variations  in  the  speed  of  the  engine 
when  the  load  is  varied,  a  contrivance  called  a  governor  is  made  use 
of.  It  usually  acts  by  opening  or  closing 
the  throttle-valve  which  regulates  the  ad- 
mission of  steam  into  the  steam-chest. 
The  simplest  form  of  governor  is  that 
invented  by  Watt,  and  its  description  will 
serve  to  illustrate  the  principle.  It  con- 
sists of  two  metal  balls  attached  to  in- 
clined arms  which  are  jointed  to  the  up- 
per end  of  a  vertical  axis.  Two  rods  are 
jointed  to  the  arms  and  to  a  collar  which 
embraces  the  axis.  The  axis  is  rotated, 
through  gearing,  by  the  main  shaft. 
When  the  engine  is  at  rest  the  balls 
hang  down  as  in  the  figure  (Fig.  48).  Flo.  48.-CENTRiP^AL  GOVERNOR 
The  balls  fly  otut  as  the  velocity  of  rota- 
tion increases,  the  collar  is  raised  and  by  means  of  levers  acts  on 
the  throttle- valve.* 

The  forms  of  governors  are  many,  and  owing  to  the  size  of  parts 
in  large  engines,  steam  governors  are  frequently  employed.  The 
governor  proper  acts  upon  a  steam  cylinder,  and  this  actuates  the 
regulating  machinery. 


Fly- Wheels. — It  has  already  been  seen  that  at  the  dead  points  the 
steam  only  presses  the  crank-axle  against  its  bearing  and  exercises 
no  rotary  effect  on  the  shaft;  the  turning  effort  varies  from  noth- 
ing at  these  points  to  its  maximum  value  when  the  crank  is  nearly 
at  right  angles  to  the  connecting  rod.  Other  causes,  as  the  varia- 
tions in  the  steam-pressure,  the  weights  of  the  piston  and  connect- 
ing rods,  also  cause  variations  in  the  driving  power,  which  produce 
variations  in  the  velocity  of  rotation.  The  effect  of  variations  in 
the  resistance  to  be  overcome  in  producing  the  same  results  has 
already  been  referred  to.  Sudden  changes  in  the  velocity  of  rota- 


*  The  governors,  instead  of  acting  on  the  throttle-valve  as  above  described, 
ore  often  arranged  to  act  by  link-motion,  directly  on  the  expansion-gearing  of 
the  slide-valve. 


114  ELEMENTARY  LESSONS  IN  HEAT. 

tion  are  injurious  to  the  mechanism  of  the  engine  because  of  the 
shocks  they  produce. 

The  object  of  the  fly-wheel  is  to  prevent  these  irregularities  oi 
motion.  It  is  a  large,  heavy  wheel,  with  the  mass  collected  as  much 
as  possible  about  the  rim.  It  receives  a  rotary  movement  from  the 
3ngine.  When  the  driving  power  is  in  excess  of  the  resistance  all 
the  moving  parts  of  the  engine  acquire  increased  velocities,  but  the 
large  moment  of  inertia  of  the  fly-wheel  prevents  a  sudden  increase 
of  velocity  and  absorbs  a  large  proportion  of  the  excess  of  energy, 
ft  small  change  in  the  angular  velocity  of  the  fly-wheel  correspond- 
ing to  a  large  amount  of  energy.  The  energy  thus  absorbed  by  the 
fly-wheel  is  restored  to  the  rotating  parts  when  the  resistance  is  in 
excess  of  the  driving  power,  and  thus  tends  to  keep  the  rotation  of 
the  shaft  uniform.  The  size  of  the  fly-wheel  is  usually  made  such 
that  the  difference  between  the  greatest  and  least  velocities  shall 
not  exceed  about  one-thirtieth  of  the  mean  velocity  for  ordinary 
machinery  and  about  one-fiftieth  for  fine  machinery. 

It  will  be  observed  that  the  governor  never  acts  until  the  change 
of  velocity  occurs  which  it  is  designed  to  control,  but  the  fly-wheel 
resists  all  change  from  its  beginning. 

In  the  above  description  we  have  supposed  a  single  cylinder. 
Two  or  more  cylinders  may  be  made  use  of,  coupled  to  the  same 
shaft  by  cranks  making  angles  with  each  other,  so  that  the  rotary 
effort  is  very  nearly  the  same  in  all  positions  of  the  shaft.  Varia- 
tions in  velocity  of  rotation,  due  to  variations  in  rotary  effort  on 
the  crank,  can  be  thus  nearly  obviated.  Locomotive  engines  are 
supplied  with  two  cylinders,  and  their  cranks  are  at  right  angles  to 
each  other.  The  variations  in  rotary  effort  may  also  be  largely 
overcome  in  the  next  form  of  engine. 

Compound  Engines. — These  are  among  the  most  efficient 
means  of  preventing  the  condensation  which  so  generally  occurs 
when  steam  is  worked  under  high  pressure  and  expansively,  and 
they  have  the  mechanical  advantage  of  nearly  equalizing  the  strain 
on  the  piston  throughout  the  stroke. 

In  these  engines  the  total  expansion  of  the  steam  is  divided 
between  two  or  more  cylinders,  so  that  the  extreme  range  of  tem- 
perature due  to  expansion  in  any  one  cylinder  is  greatly  dimin- 
ished. The  successive  cylinders  increase  in  diameter,  and,  when 


THERMO-D  TNAMICS. 


115 


the  pressure  is  very  great,  as  in  many  modern  marine  engines,  three 
and  even  four  cylinders  are  used,  giving  rise  to  triple  and  quadruple 
expansive  engines. 

In  compound  engines  there  may  be  only  one  crank  used,  in 
which  case  the  two  pistons  are  connected  with  the  same  rod,  giving 
rise  to  tandem  engines.  When  there  is  more  than  one  crank,  they 
may  or  may  not  make  angles  with  each  other.  If  there  is  but  one 
crank  or  the  cranks  are  in  the 
same  plane,  the  pistons  of  the  dif- 
ferent cylinders  rise  and  fall  to- 
gether. 

One  of  the  simplest  arrange- 
ments for  showing  the  principles  of 
the  compound  engine  of  two  cylin- 
ers  is  seen  in  Fig.  49.  In  the  up- 
ward stroke  the  steam  is  admitted 
below  in  both  cylinders,  coming 
from  the  boiler  to  the  small  or  Fm.  49.-CoMPouND  ENGINE. 

high-pressure  cylinder,  and  exhausting  from  the  upper  part  of  this 
to  the  lower  part  of  the  larger  one.  During  the  downward  stroke 
the  steam  is  admitted  at  the  upper  ends  of  the  cylinders  from  the 
same  sources.  The  high-pressure  cylinder  exhausts  into  the  larger 
one,  and  it  exhausts  into  the  condenser. 

Compound  engines  have  been  adopted  for  several  lines  of  ocean 
steamers,  where  it  is  important  to  obtain  as  much  work  as  possible 
from  a  limited  quantity  of  fuel. 

Boilers. — The  essential  parts  of  all  boilers  are  the  same,  and 
consist  of  a  furnace  in  which  the  fuel  is  burned,  a  chimney  to  pro- 
duce draught  and  carry  away  the  products  of  combustion,  a  recep- 
tacle to  hold  the  water  to  be  evaporated,  and  a  space  for  the  steam 
when  generated ;  also  fittings  to  supply  the  boiler  with  water  and 
conduct  the  steam  away  from  it  and  for  indicating  the  quantity  of 
water  present  and  the  pressure  of  the  steam. 

The  simplest  form  of  boiler  consists  of  a  cylinder  partly  filled 
with  water^  the  furnace  being  exterior  to  and  below  the  cylinder. 
But  such  forms  are  now  seldom  seen.  The  modern  forms  of  boilers 
are  numerous  and  quite  different,  depending  upon  the  conditions 
under  which  they  operate  and  the  duties  to  be  performed.  The 
objects  aimed  at  are  great  strength  in  the  boiler,  economy  in  heat- 
ing, and  large  evaporating  surface  for  the  production  of  steam.  The 


116  ELEMENTARY  LESSON 8  IN  HEAT. 

importance  of  this  last  object  has  very  generally  led  to  the  adop- 
tion of  forms  in  which  either  the  hot  gases  pass  through  numerous 
channels  entirely  surrounded  by  water,  or  the  water  and  steam  cir- 
culate in  tubes  which  are  in  the  midst  of  the  flame  and  gases  ;  the 
latter  class  is  called  tubular  boilers.  In  certain  cases  facility  in 
repairing  and  cleaning  is  of  great  importance. 

Pressure-gauges  and  Safety-valves. — The  pressure-gauge  is 
used  to  show  the  pressure  of  the  steam  within  the  boiler  at  any  time, 
It  is  connected  with  the  interior  of  the  boiler,  and  usually  indicates 
on  a  dial-plate  the  pressure  in  pounds  per  square  inch. 

The  safety-valve  is  a  circular  valve  seated  on  the  boiler,  and 
when  the  pressure  of  the  steam  exceeds  the  pressure  on  the  valve  it 
is  lifted  and  the  steam  escapes.  These  valves  may  be  loaded  di- 
rectly, or  the  load  may  be  transmitted  by  a  lever,  or  the  valve  may 
be  pressed  down  by  a  spring,  the  tension  of  the  spring  being  varied 
by  a  screw. 

Causes  of  Explosion. — Properly  adjusted  safety-valves  afford 
protection  against  the  danger  of  explosion  from  gradual  increase  of 
pressure,  but  they  are  not  always  efficient  when  there  is  a  sudden 
generation  of  steam.  There  are  several  causes  to  which  a  sudden 
evolution  of  steam  may  be  due. 

If  the  water  falls  too  low  in  the  boiler,  the  different  parts  may 
be  so  highly  heated  that  when  fresh  water  is  admitted  it  is  rapidly 
converted  into  steam  by  contact  with  the  metal.  Arrangements 
are  made  to  guard  against  this  contingency  by  having  two  cocks, 
one  a  little  above  and  the  other  a  little  below  the  level  at  which  it 
is  desired  to  maintain  the  water.  One  of  these  when  open  should 
emit  steam  and  the  other  water.  A  stout  glass  tube  opening  into 
the  boiler,  both  above  and  below  the  water  level,  and  extending 
upward  on  the  outside  constitutes  a  gauge  to  show  the  amount  of 
water  in  the  boiler. 

The  incrustations  of  boilers  due  to  the  impurities  of  the  water 
used  may  be  the  cause  of  a  violent  generation  of  steam.  This 
crust  is  a  bad  conductor,  and  the  portion  of  boiler  covered  with  it 
may  become  overheated,  when,  if  by  cracking  or  peeling  off  of  the 
crust  the  water  reaches  the  heated  metal,  there  is  rapid  evolution 
of  steam,  but  this  occurrence  could  only  produce  explosion  when 
the  limit  of  pressure  was  already  nearly  reached. 

Another  cause  of  explosion  is  probably  found  in  that  property 


THERMO-D  TNAMI08. 


117 


of  water  by  which  the  temperature  of  its  boiling  is  raised  when  it  is 
deprived  of  air ;  when  such  water  reaches  its  boiling  point,  it  bursts 
into  steam  with  explosive  violence.  Such  danger  is  to  be  appre- 
hended when  a  boiler  after  use  is  allowed  to  cool  and  again  brought 
into  action  without  the  addition  of  fresh  water. 

The  most  frequent  cause  of  explosion  is  probably  the  weakening 
of  the  boiler  due  to  natural  causes,  and  can  only  be  guarded  against 
by  inspections  and  tests. 

Feeding  Apparatus. — The  water  of  a  boiler  is  replenished  by 
means  of  force-pumps  or  injectors  or  both. 

Pumps. — Pumps  for  forcing  water  into  the  boiler  may  be  driven 
by  the  engine  itself  or  by  a  separate  engine,  the  first  method  being 
more  generally  adopted. 

Giffard's  Injector.— The  injector  is  an  instrument  which  con- 
verts the  energy  of  the  heat  in  the  steam  into  mechanical  energy 
without  the  aid  of  any  mechanism  whatever.  The  injector  is  now 
in  very  general  use.  The  method  of  its  operation  will  be  understood 
from  Fig.  50.  A  is  a  section  of  the  boiler,  B  a  pipe  leading  from 
the  steam-space  and  terminating 
in  a  nozzle,  0  is  a  pipe  leading 
from  the  water-tank,  F  a  pipe 
connected  with  the  boiler 
through  the  valve  G,  opening 
inward.  When  the  cock  at  B  is 
turned,  the  steam  rushes  out  of 
the  cone  E,  carrying  the  air  with 
it,  and  producing  a  partial  vac- 
uum in  the  tube  C.  The  water 
from  the  tank  then  rushes  up 
the  tube  C,  surrounding  the 
nozzle  and  condensing  the  es- 
caping steam.  The  particles  of  Fl°-  50-FKED  INJECTOR- 
condensed  steam  communicate  their  motion  to  the  water  particles 
by  contact  with  them,  and  the  combined  mass  is  delivered  at  high 
velocity  into  the  feed-pipe  F  and  through  the  valve  0  to  the 
boiler. 

It  at  first  sight  appears  strange  that  steam  should  be  able  to 
overcome  its  own  pressure  and  force  water  into  the  boiler  against 


118  ELEMENTARY  LESSONS  IN  HEAT. 

itself,  but  the  principle  of  action  of  the  injector  maybe  grasped  "by 
considering  the  velocities  with  which  steam  and  water  would  escape 
from  the  same  boiler.  Without  discussing  the  laws  of  gaseous  flow 
it  will  be  sufficient  to  know  that  the  velocity  of  efflux  of  steam,  in 
ordinary  boilers,  is  many  times  greater  than  that  of  water  from  the 
same  boiler, — from  twelve  to  twenty  times  as  great.  If  we  conceive 
this  steam  to  be  condensed  just  as  it  reaches  the  end  of  the  pipe  B, 
the  resulting  particles  of  water  would  travel  forward  with  the  ve- 
locity already  acquired,  and  if  these  minute  particles  could  by  any 
means  be  gathered  into  a  continuous  stream,  this  stream  would  have 
the  velocity  of  the  escaping  steam  and  would  more  than  overcome 
any  opposing  stream  of  water,  of  equal  cross-section,  escaping,  as 
such,  from  the  boiler.  This  condensed  steam  has  velocity  enough 
to  impart  considerable  energy  to  a  portion  of  the  surrounding 
water,  and  the  combined  mass  is  still  able  to  enter  the  boiler.  In 
explanation  of  the  action  it  should  be  remembered  that  the  water 
which  is  forced  in  is  less  in  volume  than  the  steam  which  issues,  so 
that,  while  the  exchange  produces  an  increase  of  mass  in  the  con- 
tents of  the  boiler,  it  involves  a  diminution  of  pressure  as  well  as 
a  fall  of  temperature. 

Condensers. — The  condenser  is  an  apparatus  into  which  the 
steam  is  discharged  when  it  has  done  its  work,  and  where  it  comes 
into  contact  with  a  spray  of  cold  water,  or  else  with  a  large  extent 
of  metallic  surface  one  side  of  which  is  cooled  by  water.  In  this 
apparatus  the  steam  is  suddenly  condensed  and  gives  up  its  heat  to 
the  water;  at  the  same  time  the  air  in  the  water  is  disengaged 
owing  to  the  small  pressure  in  the  condenser.  This  air  would  exert 
a  backward  pressure  on  the  piston  if  it  were  not  removed.  For 
this  purpose  a  pump  is  fitted  to  the  condenser  which  removes  both 
the  air  and  the  water. 

When  the  steam  does  not  come  into  direct  contact  with  the 
water,  it  is  called  surface-condensation.  A  series  of  pipes  cooled  by 
water  may  be  used  for  this  purpose.  The  steam  thus  condensed 
yields  distilled  water,  which  may  be  returned  to  the  boiler  and  re- 
peatedly used.  Such  condensers  possess  special  advantages  for 
marine  engines. 

Classes  of  Reciprocating  Engines.  —  Engines  may  be  classified  in 
various  ways : 

1.  As  regards  their  use,  as  stationary,  marine,  locomotive,  etc. 


THERMO-DTNAMICS.          .  119 

2.  As  to  the  mode  of  action,  as  condensing,  non-condensing, 
expansive,  non-expansive. 

3.  As  regards  the  manner  in  which  the  motion  of  the  piston  is 
communicated  to  the  other  parts  of  the  machinery,  as  by  a  simple 
connecting-rod,  or  by  a  beam. 

4.  As  to  the  manner  in  which  the  heat  energy  of  the  steam  is 
transformed  into  the  rotary  motion  of  the  machinery,  as  by  recip- 
rocating motion  of  the  piston  or  by  direct  rotation. 

In  this  country  the  terms  low  and  high  pressure  are  simply  used 
to  designate  engines  working  below  and  above  a  certain  pressure, 
respectively,  usually  fifty  pounds.  Neither  here  nor  elsewhere  do 
these  terms  any  longer  denote  definite  distinctions. 

Oscillating  Engines. — An  oscillating  engine  is  one  in  which  the 
cylinder  is  mounted  on  trunnions,  generally  near  the  middle  of  its 
length,  and  on  which  it  is  capable  of  oscillating  through  a  small 
arc,  so  as  to  adapt  itself  to  the  various  positions  of  the  crank,  to 
which  the  piston-rod  is  directly  connected.  The  steam  is  admitted 
from  the  boiler  through  one  trunnion,  and  passes  out  at  the  other 
through  the  exhaust-pipe  to  the  condenser.  The  valve-chests  are 
on  the  sides  of  the  cylinders  and  oscillate  with  them.  Such  en- 
gines are  economical  of  space  and  weight.  They  are  of  common 
use  in  river-boats  on  the  continent  of  Europe  and  also  in  Canada, 
and  are  used  upon  some  of  the  ferry-boats  between  New  York  and 
Brooklyn. 

Under  the  third  class  the  method  of  transmitting  the  recipro- 
cating motion  of  the  piston  by  means  of  a  walking-beam  is  gener- 
ally adopted  on  river  steamers  in  the  United  States. 

[Note  to  p.  105.] 

If  a  reversible  engine  "B"  is  not  the  most  efficient,  let  us  suppose  that  we 
have  one  "A"  of  greater  efficiency.  Let  B  take  heat  from  the  source  and 
perform  the  work  W  ;  let  A  run  B  backward  :  the  heat  taken  from  the  source 
by  B  will  then  be  restored  to  it ;  by  the  supposition  A  can  do  more  work  than 
W,  say  W" ;  therefore  in  running  B  backward  there  will  be  an  excess  of  work 
equal  to  W"  —  W. 

Since  A  requires  no  more  heat  than  B  this  operation  might  be  indefinitely 
repeated  with  an  excess  of  work  each  time  equal  to  W—  TFand  still  there 
would  be  no  change  of  temperature  in  the  source,  no  loss  of  heat.  A  produc- 
tion of  work  without  loss  of  heat  is  inconceivable  and  contrary  to  the  funda- 
mental supposition. 


120  ELEMENTARY   LESSONS  IN  HEAT. 

Turbine  Engines.  —  A  turbine  engine  is  one  in  which  the  energy 
of  expanding  steam  is  employed  to  produce  direct  rotation  in  a 
wheel  and  shaft.  The  possibility  of  thus  producing  direct  rota- 
tion was  recognized  before  the  Christian  era  and  the  principle  of 
action  was  applied  in  the  Aeolipile  of  Hero  120  B.C.  This  piece 
of  apparatus  involved  the  principle  of  one  class  of  modern  tur- 
bines, the  reaction  turbine.  The  turbine  of  Branca,  of  Loretto, 
Italy,  1629,  involved  the  principle  of  another  class,  the  impulse 
turbine,  but  it  is  only  within  the  past  twenty- five  years  that  the 
steam  turbine  has  come  to  be  considered  as  a  practical  form  of 
prime  motor.  The  turbine  engine  is  a  closer  approximation  to 
the  ideal  than  any  other  form. 

We  know  from  the  principles  of  thermodynamics  already 
discussed  that  the  useful  work  of  an  ideal  engine  would  depend 
only  upon  the  quantity  of  heat  taken  in  and  the  interval  of  tem- 
perature between  the  source  of  heat  and  the  condenser.  If  the 
temperature  of  the  condenser  be  fixed  the  useful  work  will  depend 
upon  the  quantity  of  heat  taken  in,  and  the  temperature  of  the 
source.  In  all  steam  engines  the  temperatures  of  the  source  and 
the  condenser  are  fixed  within  certain  limits,  and  the  greater 
amount  of  useful  work  is  obtained  by  having  the  temperatures  as 
far  apart  as  possible. 

This  same  statement  may  be  made  in  the  more  usual  form  as 
follows :  The  potential  energy  of  the  steam  is  derived  from  the  heat 
of  the  furnace,  this  heat  first  converts  the  water  into  steam, 
then  increases  its  temperature  and  pressure:  it  is  the  energy  due 
to  the  pressure  and  temperature  of  the  steam  that  is  available  for 
useful  work  in  the  engine.  The  larger  portion  of  the  thermic 
energy  from  the  furnace,  both  the  specific  and  latent  heat  of  the 
steam,  is  retained  by  the  exhaust  steam  and  given  up  in  con- 
densation, and  is  not  available  for  work  in  the  engine.  It  is 
therefore  evident  that  a  greater  proportion  of  the  thermic  energy 
from  the  furnace  will  be  available  the  higher  the  temperature  and 
pressure  at  which  the  steam  enters  the  engine  and  the  lower  the 
temperature  and  pressure  at  which  it  leaves  the  engine. 


THERM OD  YNA  MICS.  1 2 1 

The  rotation  in  turbines  may  be  brought  about  either  by  the 
impulsive  action  of  the  steam  particles,  moving  with  velocities 
acquired  during  the  expansion  of  the  steam  from  one  pressure  to 
another,  or  the  rotation  may  be  due  to  the  reaction  of  the  steam 
expanding  to  lower  pressure,  or  it  may  be  due  to  both  impulse  and 
reaction.  The  action  of  the  steam  turbines  is  similar  in  principle 
to  that  of  the  water  turbine,  the  motion  of  the  turbine  or  wheel  in 
each  being  due  to  the  velocity  of  flow,  or  pressure,  or  both,  of  the 
entering  fluid.  The  greater  difficulty  of  operating  steam  turbines 
efficiently  as  compared  with  water  turbines  is  due  to  the  great 
difference  in  velocities  with  which  steam  and  water  move  under 
equal  pressures.  The  velocity  of  a  jet  of  water,  escaping  into 
the  air  and  driven  by  a  pressure  of  150  Ibs.  per  sq.  inch  is  nearly 
150  feet  per  second,  while  steam  escaping  under  the  same  conditions 
has  nearly  twenty  times  this  velocity.  Steam  turbines  are  often 
run  with  boiler  pressure  from  150  to  200  Ibs  and  the  condensers  at 
a  high  vacuum  (27"  to  28"),  under  which  conditions  the  steam 
velocity  acquired  in  expanding  from  boiler  to  condenser  pressure 
would  be  over  4,000  feet  per  second. 

In  an  efficient  steam  turbine  the  pressure  and  temperature  of 
the  steam  should  be  as  high  as  practicable,  the  energy  thus 
stored  should  be  as  fully  as  possible  converted  into  mechanical 
rotation.  This  stored  energy  of  the  steam  may  be  developed 
either  by  first  converting  it  fully  into  the  kinetic  energy  of  a  moving 
jet  of  steam  and  then  transforming  this  energy  of  motion  into 
work  of  rotation,  or  the  stored  energy  may  be  only  partly 
developed  as  kinetic  energy  of  motion  and  partly  as  the  energy 
of  pressure  due  to  expansion  exerted  while  the  flow  is  taking  place. 

The,  simplest  illustration  among  successful  turbines  of  the 
first  method  of  transformation  is  shown  in  the  De  Laval  turbine. 
In  this  turbine  the  steam  expands  from  the  pressure  of  supply  to 
that  of  the  exhaust  by  a  single  step.  This  expansion  takes  place 
in  properly  shaped  nozzles  and  converts  the  available  energy  of 
the  steam  into  mass- velocity.  Issuing  from  the  nozzles  in  the 
proper  direction  the  rapidly  moving  jet  impinges  upon  concave 


122 


ELEMENTARY   LESSONS  IN  HEAT, 


vanes  located  around  the  periphery  of  the  turbine.  Fig.  51  shows 
a  section  of  a  nozzle  and  a  part  of  the  periphery  of  the  wheel  with 
eight  of  the  vanes  included.  Fig.  52  shows  a  perspective  of  the 
wheel  with  several  nozzles. 

The  conditions  for  most  efficient  action  in  a  turbine  wheel  are 
that  the  fluid  must  enter  the  wheel  without  impact  and  leave  it 
without  velocity;  that  is,  the  fluid  must  give  up  its  entire  momentum 
to  the  wheel.  The  condition  that  the  fluid  shall  leave  the  wheel 
without  velocity  requires  that  the  velocity  of  the  fluid  relatively  to  the 
wheel  at  the  point  of  discharge  shall  be  equal  to  the  velocity  of  the 


FIG.  51. — De  Laval  Nozzle  and  Blades. 

wheel  at  that  point  and  in  the  opposite  direction;  to  accomplish 
this  result  with  a  single  wheel,  the  vanes  of  the  wheel  must  move 
with  very  nearly  half  (47%)  the  speed  of  the  entering  fluid.  In  such 
a  case  it  is  evident  that  the  velocity  parted  with  by  the  steam  in 
passing  over  the  vanes  is  twice  that  of  the  vanes.  There  should  be 
no  sharp  deflections  to  suddenly  ch:;nge  the  direction  of  motion 
of  the  steam  and  as  little  friction  as  possible  between  the  stea'm  and 
vanes. 

The  condition  for  best  efficiency,  that  the  vanes  must  move  with 
half  the  speed  of  the  impinging  steam,  coupled  with  the  advan- 
tages of  working  from  high  to  low  pressure  imposes  great  speed 
in  the  De  Laval  turbine,  where  there  is  a  single  wheel  and  the 


THERMODYNAMICS.  12$ 

expansion  from  the  pressure  of  admission  to  that  of  exhaust  takes 
place  at  one  step.  A  speed  as  high  as  1380  feet  per  second  has 
been  attained  in  a  300  H.P.  turbine  of  this  class,  the  revolutions 
per  minute  reaching  10,000  and  the  diameter  of  the  wheel  30". 
The  speed  of  rotation  in  other  types  lias  reached  as  much  as  30,000 
per  minute.  These  great  speeds  are  made  possible  by  a  flexible 
shaft  which  protects  the  bearings  and  foundations  from  the  vibra- 
tions due  to  a  want  of  balance.  The  shaft  of  a  150  H.P.  engine 
of  this  pattern  is  only  one  inch  in  diameter.  To  make  use  of 


FIG.  52.— The  De  Laval  Wheel. 

such  high  speed  in  the  rotor,  gearing  is  necessary  to  transmit 
reduced  motion  to  the  machine  to  be  driven. 

This  and  similar  turbines,  whenever  the  energy  impressed  upon 
the  motor  is  derived  entirely  from  the  mass  velocity  of  the  steam 
and  not  from  the  pressure  of  expansion,  are  called  impulse  or 
velocity  turbines. 

The  Curtis  turbine  which  has  come  into  great  prominence  in 
the  U.  S.  since  1900  is  also  an  impulse  turbine.  It  is,  however, 
a  many  stage  turbine,  this  is  to  say,  that  the  steam  does  not  expand 
by  a  single  step  from  the  pressure  of  supply  to  that  of  exhaust,  but 


124 


ELEMENTARY  LESSONS   IN  HEAT. 


the  expansion  takes  place  by  stages.  In  the  first  stage  the  acting 
steam  is  expanded  from  the  boiler  pressure  to  a  certain  fraction  of 
the  range  between  the  boiler  and  exhaust  pressure;  in  the  second 
stage  through  a  fraction  of  the  remaining  pressure,  and  so  on  foi 
the  other  stages.  It  is  evident  that  in  each  stage  of  expansion  onl) 


Steam  Ckest 


NozzYe 


Moving  Blades 
Stationary  Blades 
Moving  Blades 


imvmvmwymmw 

i    ]    I     I      !     i 

FIG.  53. — Nozzles  and  Buckets,  Curtis  Turbine. 

a  part  of  the  potential  energy  of  the  steam  is  converted  into  mass 
velocity  and  it  consequently  moves  with  proportionally  lower 
speed;  a  satisfactory  velocity  of  the  vanes  or  the  peripheral  speed 
of  the  wheel  is  accordingly  much  less  than  when  the  expansion 
takes  place  through  greater  range  of  pressure.  In  this  form 


THERMODYNAMICS.  12$ 

of  turbine  the  velocity  of  the  steam  acquired  by  expanding  be- 
tween any  two  pressures  is  not  all  given  up,  as  in  the  De  Laval 
engine,  by  action  on  the  vanes  of  a  single  wheel,  but  after  actuating 
the  vanes  of  one  wheel  by  giving  to  it  a  portion  of  its  momentum, 
the  steam  passes  through  stationary  vanes  or  blades  which  change 
its  direction  and  bring  it  to  bear  at  the  desired  angle  upon  the 
vanes  of  a  second  movable  wheel,  so  that  the  steam  gives  up  an 
additional  portion  of  its  momentum  to  this  wheel;  the  steam  may 


FIG.  54.— Rotor  of  4-Stage  Curtis  Turbine. 

be  then  redirected  and  brought  to  impinge  upon  a  third  or  even 
fourth  wheel. 

The  steam  in  each  expansion  stage  parts  with  a  portion  of  its 
momentum  in  passing  over  each  row  of  vanes,  and  the  speed  of 
the  vanes  or  wheels  may  be  reduced  in  proportion  to  the  number 
of  wheels  and  still  all  the  momentum  be  extracted  from  the  steam. 

We  may  then  say  that  the  Curtis  turbine  has  three  or  four 
pressure  stages  in  each  of  which  the  pressure  is  constant  for  that 


126  ELEMENTARY  LESSONS  IN  HEAT. 

stage;  each  pressure  stage  is  sub-divided  into  two  or  three  (maybe 
more)  velocity  stages,  both  the  pressure  and  velocity  stages  serve  to 
dimmish  the  necessary  speed  of  rotation  and  still  retain  efficiency. 
The  successive  actions  in  the  Curtis  turbine  may  be  stated  as 
follows :  The  steam  passes  at  the  pressure  of  the  chest  into  a  set  of 
nozzles  at  lower  pressure  in  which  it  expands,  acquiring  full 
velocity,  and  strikes  at  the  proper  angle  against  the  vanes  of  the 
first  movable  wheel  in  this  stage  chamber.  Passing  from  the 
vanes  of  this  first  wheel,  the  steam  flows  through  and  is  redirected 
by  stationary  guide  blades  on  the  vanes  of  a  second  movable 
wheel,  then  through  another  set  of  fixed  directing  guide  blades 
on  to  another  movable  wheel,  and  so  on  over  all  the  wheels  of 
this  chamber.  After  leaving  the  last  wheel  of  this  chamber  the 
steam  collects  in  a  shallow  reservoir,  formed  by  a  steam-tight 
diaphragm  which  separates  the  first  pressure  chamber  from  the 
second.  From  this  reservoir  the  steam  passes  into  another  set  of 
nozzles  at  lower  pressure  leading  to  the  second  chamber.  It 
acquires  the  full  velocity  due  to  expansion  from  the  pressure  of 
the  first  chamber  to  that  of  the  second  and  is  directed  against  the 
vanes  of  the  first  movable  wheel  in  this  chamber;  passing  from 
the  vanes  of  this  wheel,  the  steam  has  its  direction  changed  by  the 
fixed  guide  blades  so  as  to  impinge  at  the  proper  angle  upon  the 
vanes  of  the  second  movable  wheel  and  so  on  through  the  other 
guide  blades  and  wheels  of  this  chamber  and  into  the  reservoir 
or  diaphragm'  space  adjoining  the  third  chamber.  Precisely 
similar  expansion  and  action  takes  place  through  the  remaining 
stages,  the  number  of  expansions,  of  course,  depending  upon  the 
number  of  pressure  stages.  In  the  Curtis  turbine  the  wheels 
are  of  the  same  diameter  and  being  upon  the  same  axis  have  the 
same  angular  velocity.  This  demands  that  the  steam  velocities 
developed  in  each  set  of  nozzles  shall  be  the  same  and  the  ratio  of 
expansion  in  each  set  is  arranged  to  accomplish  this  result.  Fig. 
53  shows  a  diagram  of  the  vanes  and  nozzles  in  a  two  stage  Curtis 
turbine.  The  movable  vanes  are,  of  course,  attached  to  the 


THERMO  DYNA  MICS.  *  2  7 

periphery  of  the  rotating  wheels,  the  fixed  vanes  or  blades  are 
attached  to  the  walls  of  the  cylinder  which  encloses  the  rotor. 
Fig.  54  shows  the  rotor  of  a  four  stage  Curtis  turbine  with  enclos- 
ing cylinder  removed. 

The  Parsons  turbine  engine  is  another  of  the  more  important 
of  these  engines.  It  differs  from  the  two  above  described,  in  that 
the  energy  of  the  steam  is  transmitted  to  the  movable  wheels  both 
by  the  impulse  of  motion  and  by  expansive  action.  In  this 
engine  the  expansion  from  one  pressure  to  another  does  not  take 
place  in  the  nozzles  before  coming  into  contact  with  the  turbines, 
but  the  expansion  is  taking  place  while  passing  over  the  fixed  and 
movable  blades.  A  general  idea  of  the  principle  employed  in 
actuating  the  engine  will  be  obtained  from  the  diagram,  Fig.  55, 
in  connection  with  the  following  description : 

The  engine  consists  of  an  enclosing  cylindrical  case  from  the 
interior  circumference  of  which  project  rings  of  fixed  guide-blades. 
This  case  increases  in  diameter  by  successive  steps  toward  the  low 
pressure  end.  Concentrically  within  the  case  is  mounted  the 
shaft  with  outwardly  projecting  vanes.  The  rings  of  movable 
and  fixed  blades  are  sandwiched  in  between  each  other,  the  former 
extending  nearly  to  the  outer  case  and  the  latter  in  nearly  to  the 
shaft.  The  section  of  these  vanes  is  similar  to  that  shown  of  the 
Curtis  vanes.  The  whole  may  be  considered  to  constitute  a 
large  number  of  turbine  wheels  increasing  in  diameter  toward  the 
exhaust.  It  is  clear  that  the  volume  of  the  steam  increases  in 
passing  through  each  barrel  or  drum  of  the  cylinder  as  does  also 
its  velocity.  The  movable  vanes  are  so  set  and  shaped  through- 
out the  cylinder  as  to  receive  the  benefit  of  the  increasing  velocity 
as  the  steam  strikes  them.  There  are  small  chambers,  Af  Br  Cf, 
at  the  shoulders  of  the  rotor  between  consecutive  drums  into 
which  the  steam  emerges  after  leaving  the  last  set  of  vanes  of  the 
preceding  drum.  There  the  steam  is  brought,  relatively  speaking, 
to  rest  before  it  is  directed  by  the  next  set  of  guide  blades  on  to 
the  first  set  of  moving  vanes  in  the  next  drum.  The  steam  there- 
fore expands  gradually  by  small  increments  through  the  different 
drums  before  it  reaches  the  exhaust.  In  different  sized  engines 


128 


ELEMENTARY  LESSONS  IN  HEAT. 


the  number  of  successive  rings  of  blades  may  vary  from  40  to  400, 
and  when  the  steam  leaves  the  last  ring  of  vanes  the  expansion  has 
been  completed.  The  pressure  falls  not  only  through  the  guide- 


THERMODYNAMICS.  1 29 

blades  but  in  passing  over  the  movable  vanes,  so  that  the  pres- 
sure stages  in  this  engine  are  as  numerous  as  the  rows  of  vanes 
both  fixed  and  movable.  The  steam  velocity  increases  toward 
the  lower  pressure  end  of  each  drum  and  from  drum  to  drum, 
accordingly  there  is  an  increase  of  velocity  of  the  steam  throughout 
the  turbine.  To  meet  the  conditions,  already  stated,  as  to  the 
desirable  speeds  of  the  driving  fluids  and  vanes,  the  diameters  of 
the  moving  wheels  in  the  low  pressure  drums  are  greater  than  in 
the  high  pressure. 

Steam  turbines,  of  which  the  principal  forms  have  been  briefly 
described  have  since  1895  been  steadily  replacing  the  recipro- 
cating engines  for  certain  classes  of  work.  They  are  especially 
adapted  to  operating  electric  generators  where  high  rotary  speed 
is  desired.  The  difficulty  of  securing  satisfactory  efficiency  in 
turbine  engines  while  diminishing  the  speed  of  rotation  has  been 
overcome  in  recent  improved  forms  to  such  an  extent  as  to  permit 
the  use  of  turbines  in  large  ocean  steamers. 

The  Carmania  of  the  Cunard  line  is  a  vessel  of  31,000  tons 
displacement  (672  feet  long)  and  is  driven  by  three  turbine  engines. 
The  revolutions  of  the  shaft  are  180  per  minute,  much  the  largest 
number  ever  used  in  any  vessel  of  great  size.  To  accomplish 
this  result  it  must  be  so  arranged  that  the  velocity  of  the  steam  in 
passing  from  ring  to  ring  of  vanes  is  much  less  than  in  higher  speed 
turbines,  and  this  is  brought  about  by  a  large  number  of  rings  of 
movable  and  fixed  vanes.  The  total  number  of  guiding  and 
propelling  vanes  in  the  Carmania's  turbines  is  over  1,100,000. 
There  is  building  for  the  same  company  a  vessel  760  feet  long  and 
of  88  feet  beam,  which  is  to  be  driven  by  four  turbines  aggregating 
an  indicated  H.P.  of  70,000.  The  Parsons  turbine  is  the  only 
form  that  has  yet  been  applied  to  the  propulsion  of  ocean  craft. 


CHAPTER  X. 

1ERRESTRIAL  TEMPERATURES,   AERIAL  AND  AQUEOUS 

METEORS. 

TERRESTRIAL   TEMPEKATURES. 

Temperature  of  a  Place. — The  temperature  of  a  place  is  de- 
termined by  the  readings  of  a  thermometer  placed  a  few  feet  above 
the  ground  and  protected  from  rains,  the  solar  rays,  and  all  direct 
radiation,  but  freely  exposed  to  the  air. 

Mean  Temperature  of  a  Place. — The  mean  temperature  of  a 
place  is  obtained  by  taking  a  series  of  thermometric  observations 
separated  by  equal  intervals  of  time,  and  dividing  the  sum  of  these 
observed  temperatures  by  their  number.  The  greater  the  number 
of  observations,  the  more  accurate  the  result. 

If  the  series  be  extended  at  equal  intervals  over  the  day,  the 
result  will  be  the  mean  for  the  day.  The  mean  of  the  maximum 
and  minimum  readings  for  the  day  is  often  taken  for  the  mean  of 
the  day,  but  this  is  usually  above  the  true  mean.  A  convenient 
and  close  approximation  to  the  daily  mean  may  be  obtained  by  tak- 
ing the  mean  of  the  readings  at  7  A.M.,  2  P.M.,  and  9  P.M. 

The  sum  of  the  daily  means,  divided  by  the  number  of  days  in 
the  month,  gives  the  monthly  mean,  and  the  sum  of  the  monthly 
means,  divided  by  the  number  of  months  in  the  year,  gives  the 
annual  mean  temperature.  The  sum  of  the  daily  means  through- 
out the  year,  divided  by  the  number  of  days  in  the  year,  gives  a 
more  accurate  annual  mean.  130 


AERIAL  AND  AQUEOUS  METEORS.  131 

Effect  of  Altitude  on  Temperature. — In  the  normal  condi- 
tion the  temperature  of  the  atmosphere  decreases  as  the  altitude 
increases  at  the  rate  of  about  1°  F.  for  every  300  feet,  when  the 
mean  annual  temperature  is  considered.  The  temperature  of  the 
crust  of  the  earth  increases  at  the  rate  of  about  1°  F.  for  every  53 
feet  of  descent  below  the  surface.  This  interior  heat  has  no  per- 
ceptible effect  upon  the  temperature  of  the  air. 

Isothermals  are  lines  drawn  on  a  map  through  all  points  which 
have  the  same  temperature,  and  unless  otherwise  stated  reference 
is  had  to  mean  annual  temperature,  but  of  course  isothermals  may 
be  drawn  for  months  or  seasons.  The  general  trend  of  these  lines 
is  in  an  east-and-west  direction  around  the  earth,  but  temperature 
is  influenced  by  so  many  local  causes  that  they  are  seldom  parallel 
to  the  equator.  Their  directions  with  reference  to  the  parallels  are 
modified  by  the  proximity  of  places  to  large  bodies  of  water,  by 
the  direction  of  ocean  currents,  by  the  prevailing  direction  of  the 
winds,  and  by  the  altitude  and  configuration  of  the  land  areas. 
Places  near  the  sea  have  higher  winter  and  lower  summer  tempera- 
tures than  places  of  the  same  latitude  and  altitude  in  the  interior 
of  continents.  Since  temperature  is  the  most  important  element 
in  climate,  the  same  influences  which  affect  temperature  affect  cli- 
mate. Ocean  and  insular  climates  are  more  uniform  than  conti- 
nental climates. 


AERIAL   AND    AQUEOUS   METEOKS. 

These  phenomena  are  so  dependent  upon  heat  agencies  that  a 
brief  outline  of  the  more  important  and  common  of  them  is  deemed 
appropriate  here. 


AERIAL   METEORS. 

These  include  all  the  phenomena  resulting  from  the  motions 
of  the  atmosphere  relatively  to  the  earth.  Such  motions  are  called 
winds.  All  winds  are  primarily  due  to  differences  of  pressure  in 
the  atmosphere,  and  these  may  be  due  to  differences  of  temperature, 
differences  in  the  amount  of  aqueous  vapor  present,  arid  (to  a  slight 


132  ELEMENTARY  LESSONS  IN  HEAT. 

extent)  to  differences  of  density.  The  main  cause  of  winds,  how- 
ever, is  the  difference  of  temperature,  which  also  produces  differ- 
ence of  density.  Without  the  differences  of  temperature  which 
exist  over  the  earth's  surface,  it  is  probable  that  the  earth's 
atmosphere  would  be  in  a  quiescent  condition. 


GENERAL   OB   PLANETARY   CIRCULATION    OF   THE   ATMOSPHERE. 

Owing  to  the  permanent  differences  of  mean  temperature  on  the 
earth's  surface  caused  by  differences  of  latitude,  the  air  over  the 
tropical  regions  is  warmer  than  that  over  the  northern  and  southern 
regions.  This  warm  air  being  more  expanded  ascends  and  flows 
over  above  both  to  the  north  and  south,  while  cold  air  flows  in 
toward  the  equator  from  both  sides  below. 

In  this  connection  it  should  be  borne  in  mind  that  while 
unequal  pressure  is  necessary  to  produce  motion  in  the  air,  this 
inequality  of  pressure  need  not  prevail  at  all  levels,  for  while  the 
total  pressure  in  two  regions  at  different  temperatures  may  be  the 
same  at  one  level,  this  equality  of  pressure  cannot  exist  at  any 
other  level  within  these  regions.  The  reason  for  this  is  that,  since 
the  density  of  the  warm  air  is  less,  the  decrease  of  pressure  for  a 
given  increase  of  height  is  greater  in  the  cold  than  in  the  warm 
region,  consequently  in  the  cold  region  the  pressure  is  greater  below 
and  less  above  the  level  of  equal  pressure.  An  interchange  of  air 
will  therefore  take  place  between  two  such  regions,  the  winds  blow- 
ing in  opposite  directions  on  the  two  sides  of  the  surface  of  equal 
pressure.  If  the  level  of  equal  pressure  be  at  the  earth's  surface, 
the  interchange  will  still  occur,  for  the  excess  of  pressure  at  all 
points  above  the  surface  in  the  warm  area  will  cause  the  upper  air 
to  flow  from  that  region,  this  will  diminish  the  total  pressure  at  the 
earth's  surface  in  the  warm  region,  and  consequently  the  lower  air 
will  move  from  the  cold  to  the  warm  region.  It  is  evident  from 
the  statements  above  made  that  the  conditions  necessary  to  an  in- 
terchange of  air  between  the  tropical  and  polar  regions  of  the  earth 


AERIAL  AND  AQUEOUS  METEORS.  133 

are  always  present  and  operative,  and  the  winds  thus  produced  con- 
stitute the  general  circulation. 

The  principle  which  causes  the  general  circulation  has  frequent 
application  in  the  production  of  local  winds.  It  may  be  readily 
illustrated  by  placing  a  candle  near  the  top  and  another  near  the 
bottom  of  a  door  connecting  two  rooms  at  different  temperatures. 
When  the  door  is  opened,  the  flame  of  the  upper  candle  will  be 
blown  toward  and  that  of  the  lower  will  be  blown  from  the  cold 
room. 

The  general  circulation  which  would  result  from  the  tempera- 
ture distribution  due  to  latitude  alone  is  materially  modified  and 
complicated  by  the  arrangement  of  land  and  water  and  by  the 
varying  rotational  velocities  of  the  earth's  surface  as  we  pass  from 
the  poles  to  the  equator,  thus  giving  rise  to  the  wind  systems  that 
actually  exist. 

FERREL'S   YIEW   OF   THE    GENERAL   CIRCULATION. 

The  theory  of  the  general  or  planetary  circulation  of  the  at- 
mosphere which,  with  some  modification,  has  met  with  most  gen- 
eral acceptance  by  meteorologists  was  first  set  forth  in  this  country 
by  Prof.  Wm.  Ferrel.  It  is  believed  that  to  him  more  than  to  any 
other  individual  the  theory  owes  its  origin  and  development.  His 
discussion  is  a  profound  one,  and  constitutes  a  volume  of  itself; 
it  is  difficult  of  simple  or  disconnected  treatment;  however,  his 
views  are  to  a  certain  extent  capable  of  condensation,  and  give  sat- 
isfactory general  ideas. 

Assuming  that  the  permanent  difference  of  temperature  be- 
tween the  equatorial  and  polar  regions  causes  an  interchange 
of  ah  between  them  (and  there  can  be  little  doubt  that  it  does 
produce  such  an  exchange),  and  assuming  also  that  the  initial 
condition  of  the  air  is  one  of  relative  rest  when  the  interchanging 
motion  begins,  and  that  the  air  is  without  friction  against  the 
earth,  Prof.  Ferrel  has  shown  that,  under  these  circumstances,  the 
different  rotational  velocities  of  the  earth's  surface,  coupled  with 
the  interchanging  motion  of  the  air,  will  involve  the  entire  mass  of 
air  between  the  parallels  of  35°  on  both  sides  of  the  equator  in  a 
westward  motion  of  considerable  velocity,  and  that  over  the  rest  of 
the  surface  of  the  earth  in  an  eastward  motion  which  will  be  of 


134  ELEMENTARY  LESSONS  IN  HEAT. 

much  greater  velocity  in  high  latitudes.*     He  has  shown  that  the 

p  ^  deflections   which   the    moving  air 

will  experience  due  to  this  motion, 
being  to  the  right  in  the  northern 
hemisphere  and  to  the  left  in  the 
southern,  will  cause  the  depth  and 
pressure  of  the  air  to  be  greatly 
diminished  at  the  poles,  producing 
a  virtual  vacuum  there,  and  consid- 
erably diminished  at  the  equator, 

FIG.  51.-EABTH  WITH  FRICTIONS"    and  increased   at    the   parallels    of 

ATMOSPHERE.  35°^  where  the  velocity,  of  the  air 

changes  sign,  the  velocity  being  westward  between  these  parallels 

and  eastward  outside  of  them.     Under  these  conditions  a  section 

of  the  earth  and  atmosphere  would  be  as  shown  in  Fig.  51. 

Now,  in  the  actual  case  of  the  earth  and  atmosphere,  witli 
friction  against  the  surface  and  an  interchanging  motion,  there 
would  be  a  tendency  toward  the  same  state  of  affairs,  but  the 
deflecting  forces  are  so  modified  by  friction  that  the  diminution  of 
depth  and  pressure  at  the  poles  and  at  the  equator  are  but  slight, 
and  there  is  but  a  small  increase  at  about  the  parallel  of  30°. 
That  there  must  be  a  tendency  to  the  same  state  of  affairs  as  when 
there  was  no  friction  is  evident  because  friction  could  not  operate 
until  the  motions  which  produced  the  former  condition  had  com- 
menced. In  this  actual  case,  also,  the  entire  mass  of  air  between 
the  belts  of  high  pressure  has  not  a  westward  velocity  as  in  the  first 
case,  but  at  great  altitudes  this  air  has  eastward  velocity.  The 
relative  amounts  of  easterly  and  westerly  motion  at  the  earth's  sur- 
face in  this  actual  case  will  depend  upon  the  condition  that  the 
sum  of  the  moments  of  gyration  arising  from  the  action  of  the  air 
by  friction  upon  the  earth  over  the  entire  surface  must  be  equal  to 
zero,  or  else  the  velocity  of  the  earth's  rotation  would  be  affected. 

In  this  explanation  it  will  be  observed  that  the  accumulation  of 
air  at  the  limiting  parallels  and  its  diminution  at  the  poles  are  due 
to  the  deflections  caused  by  the  earth's  rotation,  which  press  the 


*  Many  years  after,  though  without  a  knowledge  of  Ferrel's  work,  Prof. 
Werner  Siemens  deduced  the  same  limiting  parallels  as  here  given.  Sitzungs- 
berichte,  March  4,  1886;  Phil.  Mag.,  June,  1886. 


AERIAL  AND  AQUEOUS  METEORS. 


135 


moving  air  from  both  sides  toward  these  parallels.  The  belts  of 
high  pressure  near  the  tropics  are  therefore  the  unavoidable  results 
of  an  interchanging  motion  on  a  rotating  globe  between  the  polar 
and  the  equatorial  regions.  The  accumulation  is  more  largely  due 
to  the  greater  deflection  in  the  upper  atmosphere,  where  the  motion 
is  greater  and  the  resistance  less  ;  hence  this  accumulation  causes 
the  air  to  flow  out  from  beneath,  where  the  tendency  to  heap  it  up 
is  less,  both  toward  the  poles  and  toward  the  equator.  It  will  be 
observed  also  that  the  deflections  which  cause  the  tropical  high- 
pressure  belts  likewise  produce  a  diminished  pressure  in  the  polar 


FIG.  52.— GENERAL  ATMOSPHERIC  CIRCULATION.    (AFTER  FERREL.) 


regions,  but  not  a  belt  of  low  pressure  about  the  polar  circles,  as  has 
been  supposed  to  exist. 

According  to  Ferrel's  view,  then,  we  summarize  the  most  prob- 
able circulation  of  the  air  to  be  as  indicated  in  the  figure  (Fig.  52). 
The  upper  strata  move  poleward,  and  the  lower  strata  the  reverse, 
except  that  in  the  middle  latitudes  there  is  a  thin  stratum  at  the 
earth's  surface,  deflected  from  beneath  the  parallels  of  high  press- 


136  ELEMENTARY  LESSONS  IN  HEAT. 

are,  moving  poleward.  This  surface  current,  however,  does  not 
extend  all  the  way  to  the  pole,  but,  being  interfered  with  by  a  sur- 
face current  from  the  pole,  it  gradually  ascends,  and  returns  toward 
the  equator  in  a  stratum  higher  up  but  below  the  poleward  strata 
of  the  upper  atmosphere.  FerrePs  view  of  the  planetary  circulation 
and  his  explanation  of  the  tropical  belts  of  high  pressure  have, 
until  recently,  been  very  generally  accepted. 

The  data  of  the  U.  S.  weather  bureau,  collected  in  connection 
with  the  weather  service  and  with  international  cloud  observations, 
which  data  have  been  tabulated  and  very  ably  discussed  by  Prof. 
F.  H.  Bigelow,  show  that  Ferrel's  view  of  the  general  circulation 
needs  to  be  modified  in  several  respects.  The  modifications  thus 
suggested,  in  the  above  outline,  refer  especially  to  the  interchange 
of  air  between  the  equatorial  and  polar  regions.  According  to  Fer- 
rel  the  equatorial  warmer  air  flows  poleward  mostly  at  high  alti- 
tudes, above  five  miles,  and  that  below  this,  and  above  the  surface 
winds,  there  is  a  sheet  of  cold  air  flowing  from  the  northwest 
toward  the  equator. 

The  conclusions  of  Prof.  Bigelow  from^  observed  cloud  motions 
are  that  this  interchange  of  air  between  warm  and  cold  latitudes 
takes  place  over  the  United  States  almost  entirely  below  the  three- 
mile  level,  and  is  accomplished  by  counter-currents  of  warm  and  cold 
air  advancing  alternately  from  north  and  south  ;  that  above  the 
three-mile  level  there  is  but  little  interchanging  motion  between 
north  and  south,  and  that  the  circulation  of  the  upper  air  is  nearly 
east  and  but  little  affected  by  the  interchanging  north  and  south 
currents  below.  According  to  this  view  the  tropical  energy  is  ex- 
pended in  forcing  the  equatorial  air  northward  in  a  succession  of 
currents  at  low  altitudes,  rather  than  expanding  it  to  great  alti- 
tudes and  sending  it  northward  in  a  continuous  sheet;  the  cold 
air  also  returns  by  currents,  the  currents  from  the  opposite  direc- 
tions moving  at  about  the  same  level  instead  of  at  different  levels. 
These  counter-currents  result  from  the  mechanical  tendency  of 
the  air  to  maintain  an  equilibrium  between  the  warm  masses  over 
the  equator  and  the  cooler  masses  to  the  north.  The  conclusions 
of  Prof.  Bigelow  seem  to  be  well  founded  so  far  as  the  United 
States  is  concerned. 


AERIAL  AND  AQUEOUS  METEORS.  137 


SYSTEM   OF   WINDS. 

The  above  view  of  the  general  circulation  roughly  outlines  three 
zones  in  each  hemisphere  which  approximately  correspond  with 
the  adopted  wind  systems  at  the  earth's  surface. 

TJie  Equatorial  System  or  Trade-  Winds. — These  winds  prevail 
at  the  earth's  surface  approximately  between  the  parallels  of  30° 
north  and  30°  south  latitude,  and  flow  toward  the  equator.  Their 
direction  \sfrom  the  northeast  in  the  northern  and /row  the  south- 
east in  the  southern  hemisphere,  becoming  more  easterly  as  they 
approach  the  equator.  Between  the  trades  in  the  two  hemispheres 
is  a  region  of  calms  or  variable  winds,  from  three  to  ten  degrees 
wide.  This  equatorial  calm-belt  constitutes  the  doldrums.  The 
central  line  of  the  belt  oscillates  with  the  seasons,  being  one  or  two 
degrees  north  of  the  equator  in  the  spring  and  nine  or  ten  degrees 
north  in  the  summer.  The  direction  of  the  trades  at  the  border  of 
the  calms  is  nearly  westward,  the  northern  trades  blowing  more  to 
the  westward  than  the  southern.  , 

These  winds  may  be  directly  ascribed  to  two  causes:  first,  the 
two  belts  of  high  barometer  or  great  atmospheric  pressure  which 
encircle  the  earth  at  about  the  parallel  of  32°  in  the  northern  and 
25°  in  the  southern  hemisphere  with  a  decrease  of  pressure  toward 
the  equator,  these  belts  of  high  pressure  resulting  from  the  general 
circulation  as  described;  second,  the  higher  mean  temperature  of 
the  air  at  and  near  the  equator.  Both  these  conditions  cause  the 
air  within  the  limiting  parallels  to  move  toward  the  equator, 
the  direction  of  motion  being  modified  as  stated  by  the  earth's 
rotation. 

Winds  of  the  Temperate  Regions. — Beyond  the  northern  and 
southern  borders  of  the  trades  in  the  two  hemispheres,  over  a  belt 
of  from  twenty-five  to  thirty-five  degrees,  the  prevalent  winds  at 
the  earth's  surface  are  from  the  westward  and  blow  toward  the 
poles.  In  the  northern  hemisphere  they  blow  from  a  point  a  little 
south  of  west,  and  in  the  southern  hemisphere  from  a  little  north 
of  west,  being  more  nearly  west  at  the  centre  of  the  belt.  These 
winds  are  sometimes  designated  as  passage-winds. 

These  winds  are  also  directly  attributable  to  the  belts  of  high 
pressure  mentioned.  From  beneath  these  belts  the  surface  air 


138  ELEMENTARY  LESSONS  IN  HEAT. 

flows  toward  the  poles  as  well  as  toward  the  equator,  so  that  the 
prevailing  direction  of  the  surface  winds  is  from  the  southwest. 
In  the  temperate  regions  of  the  continents,  and  especially  in  North 
America,  the  interchanging  currents  already  referred  to,  and  the 
local  conditions,  greatly  disturb  the  uniformity  of  the  system. 

Winds  of  the  Polar  Regions. — Beyond  and  to  the  north  of 
the  areas  swept  by  the  passage-winds  in  the  northern  hemisphere 
the  atmospheric  motions  are  very  uncertain.  Prof.  Ferrel  indicates 
this  as  a  region,  of  polar  calms,  though  there  are  known  to  issue 
from  these  regions  winds  blowing  to  the  southward  at  certain 
seasons. 

Motions  of  the  Upper  Atmosphere. — It  will  be  observed  that  the 
winds  above  referred  to  are  those  at  the  earth's  surface.  Now,  the 
principle  of  continuity  evidently  requires  that  the  mass  of  air  mov- 
ing in  one  direction  over  any  parallel  must  just  equal  that  moving 
in  the  opposite  direction,  otherwise  the  atmosphere  would  be  grad- 
ually drawn  from  certain  portions  of  the  earth's  surface  and  accu- 
mulated at  others. 

We  should  therefore  expect  to  find  the  winds  at  certain  heights 
in  the  areas  embraced  in  the  above  systems  blowing  in  directions 
in  general  opposite  to  those  at  the  earth's  surface,  and  such  is  the 
case.  The  ejected  ashes  from  volcanoes  situated  in  the  tropical 
regions  have  been  carried  long  distances  by  the  upper  currents  in 
a  direction  opposite  to  that  of  the  prevailing  surface  winds.  Fine 
dust,  supposed  to  be  peculiar  to  certain  regions,  has  been  found  at 
long  distances  from  these  regions,  and  is  believed  to  have  been 
lifted  into  the  upper  air  and  transported  by  the  higher  tropical 
currents  whose  directions  are  thus  given.  Lastly,  on  the  peaks  of 
several  high  mountains  direct  observations  show  that  the  winds  of 
the  upper  regions  are  often  blowing  from  the  equator  and  come 
from  the  southwest,  while  the  trades  at  the  base  of  the  mountains 
blow  toward  the  equator  and  from  the  northeast. 

By  observations  it  is  found  that  in  the  temperate  regions,  above 
the  prevailing  winds  from  the  southwest,  the  wind  frequently 
moves  toward  the  equator.  In  the  polar  regions  the  meridianal 
interchange  of  air  both  at  high  and  low  altitudes  takes  place  very 
gradually. 

Directions  of  the  Winds  in  the  General  Circulation. — The  east- 
erly and  the  westerly  components  of  motion  of  the  winds  in  all  the 


AERIAL  AND  AQUEOUS  METEORS.  139 

general  systems  depend  upon  a  principle,  susceptible  of  demonstra- 
tion, that,  owing  to  the  rotation  of  the  earth  on  its  axis,  there  arises 
a  force  which  tends  to  deflect  all  motions  in  the  northern  hemi- 
sphere to  the  right  and  in  the  southern  hemisphere  to  the  left, 
supposing  the  observer  to  face  in  the  direction  of  motion.  This 
force  varies  with  the  latitude,  being  nothing  at  the  equator  and 
greatest  at  the  poles,  and  is  not  limited  in  action  to  bodies  moving 
north  and  south,  as  is  frequently  supposed,  but  extends  to  all  mo- 
tions, even  to  those  along  the  parallels.  The  trade-winds  moving 
toward  the  equator  are  thus  swerved  toward  the  west,  the  passage- 
winds  moving  from  it  are  swerved  to  the  east,  the  polar  winds  mov- 
ing toward  the  equator  would  also  tend  to  the  west. 

Local  Winds. — The  general  circulation  of  the  atmosphere  which 
has  been  described  is  in  many  places  materially  and  regularly  modi- 
fied by  local  conditions  producing  uniform  results.  Among  the 
most  important  of  these  are  the  periodic  winds. 

1.  Periodic  Winds. — Land  and  Sea  Breezes. — These  are  the 
well-known  daily  alternating  breezes  which  prevail  along  the  coasts 
of  islands  and  continents.  These  winds  are  most  marked  in  tropical 
countries,  but  also  prevail  far  outside  these  limits.  In  the  daytime 
they  blow  from  the  water  to  the  land,  and  at  night  in  the  reverse 
direction.  This  is  due  to  the  fact  that  while  the  sun  is  shining  the 
land  becomes  warm  quicker  than  the  water,  and  at  night  it  also 
cools  more  quickly.  The  air,  deriving  its  heat  from  the  surface 
beneath,  is  consequently  cooler  and  heavier  over  the  water  during 
the  day,  and  warmer  and  lighter  soon  after  sunset;  consequently 
the  directions  of  the  breezes  are  as  stated.  It  must  be  observed  that 
these  breezes  depend  primarily  upon  the  diurnal  variations  of  tem- 
perature, and  secondarily  upon  the  greater  mobility  of  the  water  and 
the  greater  depth  to  which  the  heat-rays  will  penetrate  it,  its  great 
latent  heat,  and  the  absorptive  power  of  the  water  vapor  which  is 
more  abundantly  present  over  the  water, — properties  tending  to 
prevent  rapid  changes  of  temperature.  The  simple  difference  of 
specific  heats  between  land  and  water  does  not  have  the  great  effect 
usually  assigned  it. 

Monsoons. — The  annual  variations  of  temperature  accompanying 
the  changing  seasons  also  have  their  effect  in  modifying  the  prevail- 


140  ELEMENTARY  LESSONS  IN  HEAT. 

ing  winds.  During  one  portion  of  the  year  the  winds  blow  toward 
the  continents,  and  during  the  remainder  from  them.  Among  the 
most  remarkable  of  such  winds  are  the  monsoons,  those  winds 
which  blow  from  the  Indian  Ocean  over  Southern  Asia  during  the 
warmer  half  of  the  year  and  in  the  opposite  direction  during  the 
other  half.  The  difference  of  temperature  between  the  continent 
and  sea  is  the  cause  of  them.  The  former  of  these  winds,  passing 
over  the  mountains  of  Hindostan,  have  their  moisture  condensed, 
giving  a  region  of  excessive  rainfall. 

Similar  winds  are  produced  in  every  part  of  the  world  near  the 
coasts  of  extensive  land  areas.  In  the  United  States  they  are  ob- 
served merely  as  modifying  the  direction  of  the  prevailing  winds. 
This  is  the  case  on  both  the  eastern  and  the  western  coasts,  and  in 
Florida  the  winds  are  in  opposite  directions  in  summer  and  winter, 
and  are  by  some  deemed  sufficiently  constant  to  be  classed  as  mon- 
soons. 

Mountain  Breezes. — Very  often  in  the  ravines,  gulches,  and 
narrow  valleys  of  mountain  regions,  distinct  day  and  night  breezes 
are  felt.  Those  at  night  are  due  to  the  more  rapid  cooling  by  radi- 
ation of  the  peaks,  spurs,  and  higher  ridges,  which  in  turn  cool  the 
air  and  cause  it  to  flow  down  through  the  ravines  into  the  valleys. 
In  the  morning  the  higher  surfaces  are  first  touched  and  warmed 
by  the  sun,  and  the  tendency  is  for  the  air  to  flow  up  the  ravines. 
The  action  here  is  the  same  as  in  the  case  of  land  and  sea  breezes, 
the  plain  at  the  base  of  the  slope  taking  the  place  of  the  ocean. 
Generally  the  winds  which  pass  over  high  mountains  are  deprived 
of  their  moisture  and  reduced  in  temperature,  but  reference  is  hero 
had  only  to  the  local  currents  due  to  daily  variations  of  tempera- 
ture in  small  adjoining  areas. 

In  addition  to  these  regular  winds  there  are  other  local  dis- 
turbances which  depend  upon  a  fundamental  principle  that  is  to  n 
greater  or  less  degree  concerned  in  many  of  the  atmospheric, 
motions  ;  to  this  principle  we  shall  now  allude. 

Stable  and  Unstable  Condition  of  the  Atmosphere. — In  the 
normal  condition  of  the  atmosphere  we  may  consider  it  arranged 
in  concentric  spherical  layers  around  the  earth,  the  densest  and 
warmest  layers  being  below.  The  temperature  of  the  air,  as  we 
have  seen,  decreases  on  an  average  about  1°  F.  for  every  300  feet 
of  ascent.  If  a  volume  of  air  from  the  lower  strata  be  moved  up- 


AERIAL  AND  AQUEOUS  METEORS.  141 

ward,  it  will  expand,  owing  to  the  diminution  of  pressure  at  higher 
levels.  This  expansion  will  cool  the  air  about  1°  F.  for  every  186 
feet  of  upward  motion.  In  the  normal  condition  of  the  atmosphere, 
then,  the  decrease  of  temperature  due  to  the  expansion  that  would 
occur  in  a  volume  of  air  moving  upward  is  more  rapid  than  the  de- 
crease of  temperature  in  the  surrounding  air  due  to  change  of  level. 
If,  therefore,  an  unconfined  volume  of  the  dense,  lower  air  could 
be  forced  upward  through  the  higher  strata,  its  temperature  would 
decrease,  due  to  expansion,  at  the  rate  of  1°  F.  for  every  186  feet 
of  its  ascent,  and  it  would  be  cooler  at  any  level  than  the  surround- 
ing air  at  the  same  level  and  consequently  heavier  than  an  equal 
volume  of  that  air,  In  the  above-stated  case  the  air  is  in  a  condi- 
tion of  stable  equilibrium,  and  if  disturbed  would  tend  to  return 
to  the  original  condition. 

But  this  normal  state  of  the  atmosphere  does  not  always  exist. 
On  still,  hot  days  in  warm  regions  the  lower  layers  of  the  air  be- 
come very  much  warmer  than  those  above,  so  much  so  that  the  rate 
of  decrease  of  temperature  upward  is  much  greater  than  1°  F.  for 
every  300  feet.  Whenever  this  decrease  of  temperature  upward 
becomes  greater  than  that  due  to  expansion,  or  greater  than  1°  F. 
for  186  feet  of  ascent,  the  condition  of  stable  equilibrium  is  de- 
stroyed, and  a  volume  of  the  lower  air  moving  upward  would  be 
warmer  than  the  surrounding  air  at  the  same  level,  and  conse- 
quently lighter  than  an  equal  volume  of  it.  In  this  case,  then,  if 
a  volume  of  the  lower  air  were  to  start  upward,  it  would  not 
tend  to  return  to  its  original  position,  but  would  continue  upward 
until  its  temperature  became  the  same  as  that  of  the  surrounding 
air. 

Whirlwinds. — Under  this  head  may  be  included  the  very  sud- 
den and  local  whirls  produced  by  the  meeting  of  rapid  currents 
from  different  directions,  as  they  pass  along  streets  or  other  natural 
channels,  such  as  gorges  or  ravines  in  irregular  and  mountainous 
regions.  These  are  like  eddies  in  the  running  stream.  There  is, 
however,  a  typical  whirlwind  peculiar  to  a  quiet  atmosphere  which 
deserves  attention.  This  is  of  frequent  occurrence  in  still,  hot,  arid 
regions,  and  is  a  familiar  sight  to  all  who  have  had  experience  on 
the  plateau  and  basin  regions  of  our  western  territory,  besides  being 
of  more  rare  occurrence  in  nearly  all  parts  of  the  country.  The 
perfect  type  of  this  wind  is  often  seen  on  hot,  still  days  in  the  dry, 


142  ELEMENTARY  LESSONS  IN  HEAT. 

dusty  valleys  of  the  Utah  and  Nevada  basins.  In  these  arid  val- 
leys, during  the  hottest  part  of  a  quiet  summer  day,  the  observer 
may  often  see  several  tall,  slender  columns  of  dust,  varying  from  one 
hundred  to  more  than  one  thousand  feet  in  height,  travelling  across 
the  dusty  flats. 

Observations  show  that  these  disturbances  begin  in  a  whirling 
movement  which  extends  spirally  upward.  The  origin  and  contin- 
uance of  these  whirls  in  an  apparently  still  atmosphere  are  due  to 
the  disturbance  of  the  normal  equilibrium  of  the  air  brought  about 
by  the  greater  heating  which  the  lower  strata  receive  from  their 
contact  with  the  earth.  These  strata  become  very  warm,  and  press 
upward  against  the  overlying  strata  ;  finally  an  opening  is  made 
through  them,  and  the  hot  air  flows  in  from  all  sides  toward  this 
outlet  to  reach  a  region  of  less  pressure. 

The  whirling  motion  is  the  result  of  a  lack  of  absolute  homo- 
geneity of  physical  condition  in  the  surrounding  air  and  of  equal 
smoothness  of  the  earth's  surface.  These  cause  the  inblowing  air  to 
depart  from  radial  lines,  and  the  direction  of  turning  will  be  deter- 
mined by  the  strongest  current.  The  whirling  once  begun  is  con- 
tinued by  the  centrifugal  force  developed  by  it.  In  these  winds  the 
direction  of  turning  is  not  fixed,  but  depends  upon  local  incidents. 
The  volume  perceptibly  involved  in  the  motion  generally  extends 
only  a  few  feet,  though,  of  course,  these  winds  vary  in  strength  and 
extent.  The  upward  motion  of  the  air  will  continue  until  the  tem- 
perature of  the  ascending  air  is  brought  by  expansion  to  that  of  the 
surrounding  air  of  the  same  level,  when  it  will  spread  itself  among 
the  strata  above.  The  progressive  motion  of  the  spiral  column  is 
probably  due  to  a  slight  general  motion  of  the  air  in  which  the 
whirl  occurs,  especially  of  the  upper  layers.  Theoretically  these 
whirls  would  continue  until  the  heated  air  below  had  escaped  up- 
ward through  the  whirl,  or  as  long  as  the  difference  of  temperature 
between  the  lower  air  and  the  strata  above  was  greater  than  1°  F. 
for  every  186  feet  of  ascent,  but  ordinarily  their  progressive  motion 
takes  them  beyond  the  limits  of  the  areas  fulfilling  the  conditions 
for  their  existence. 

2.  Storms. — Besides  the  general  circulation  and  the  more  local 
winds  which  have  been  referred  to,  there  are  transient  disturbances 
of  widely  varying  extent  and  energy  which  are  classed  under  the 


AERIAL  AND  AQUEOUS  METEORS.  143 

general  head  of  storms.  Many  of  these  involve  both  local  and  gen- 
eral influences  and  in  some  cases  may  to  a  limited  extent  be  consid- 
ered as  part  of  the  general  circulation.  Certain  of  these  storms 
will  be  briefly  considered. 

Cyclones. — This  term  is  applied  to  those  violent  whirlwinds  of 
great  extent,  involving  large  volumes  of  air  in  their  action, sometimes 
extending  over  elliptical  areas  two  thousand  miles  or  more  in  axial 
direction,  continuing  for  many  days  and  travelling  for  great  dis- 
tances. 

It  has  long  been  known  that  the  depth  of  the  mass  of  air  in* 
volved  in  these  cyclones  is  generally  very  small  as  compared  to  it? 
horizontal  extent,  the  relation  being  often  as  1  to  500,  and  fre- 
quently even  a  greater  difference.  The  difficulty  which  meteorolo- 
gists have  had  to  solve  is  to  satisfactorily  account  for  the  energy 
which  is  unquestionably  expended  in  cyclones,  the  energy  necessary 
to  keep  in  rapid  rotation  such  an  enormous  mass  of  air  as  is 
generally  involved  in  a  cyclone. 

The  theory  which,  to  within  recent  years,  has  been  most  gener- 
ally accepted  as  offering  the  best  explanation  of  the  cyclone  is 
known  as  the  convectional  or  condensation  theory.  This  theory 
supposes  that  the  energy  of  the  cyclone  is  mainly  latent  in  the  aque- 
ous vapor  of  the  air,  and  also  to  a  small  extent  in  the  expanded  strata 
of  the  unstable  atmosphere  in  which  the  cyclone  originates  and  is 
propagated.  The  theory  assumes  that  if  in  an  atmosphere  moist 
and  in  unstable  condition  there  is  produced  an  ascending  current  at 
any  point,  the  air  rises,  as  in  the  case  of  the  desert  whirl,  with  this 
very  marked  difference  :  in  the  case  under  consideration  the  ascend- 
ing air  would  be  cooled  by  the  expansion  due  to  the  diminished  pre^- 
sure,  as  in  the  whirlwind,  but,  as  soon  as  a  sufficient  reduction  of 
temperature  takes  place,  condensation  of  the  aqueous  vapor  would 
begin,  with  liberation  of  its  latent  heat.  Therefore,  the  rapidity  of 
cooling  with  ascension  is  diminished  by  continuous  conversion  of 
the  latent  heat  of  aqueous  vapor  into  sensible  heat.  The  condition 
of  unstable  equilibrium  in  such  air  is  therefore  reached  with  a  much 
smaller  decrement  of  temperature  than  in  dry  air.  The  difference 
of  temperature  between  the  ascending  column  and  the  surrounding 
air  is  accordingly  greater  than  if  the  vapor  were  not  present.  Be- 
cause of  this  greater  difference  of  temperature  at  the  same  levels, 
the  upward  draught  would  be  much  more  violent  and  would  extend 


144 


ELEMENTARY  LESSONS  IN  HEAT. 


to  a  greater  height.  As  the  ascent  is  continued,  the  aqueous  vapor 
is  condensed  into  clouds  or  falls  as  rain,  and  the  ascending  air  over- 
flows in  all  directions  from  the  upper  end  of  the  aerial  chimney, 
and  spreads  over  the  adjoining  area.  The  overflow  diminishes  the 
pressure  beneath  the  up-draught  and  increases  it  in  the  annular 
area  surrounding  it,  both  of  which  causes  tend  to  increase  the 
draught. 

In  the  case  now  under  consideration  the  great  amount  of  heat 
latent  in  the  aqueous  vapor  existing  in  the  lower  air  and  which  be- 
comes sensible  heat  by  condensation  makes  a  difference  in  degree 
but  not  in  principle  between  the  action  in  the  cyclone  and  whirl- 
wind. 


FIG.  53.— CYCLONIC  MOTION,  NORTHERN  HEMISPHERE. 

Under  these  conditions  the  air  would  flow  from  all  directions 
toward  the  low-pressure  centre,  but  by  the  rotation  of  the  earth 
would  be  deflected  around  it  as  indicated  in  Fig.  53,  the  winds 


AERIAL  AND  AQUEOUS  METEORS.  145 

in  the  northern  hemisphere  always  circulating  in  a  counter-clock- 
wise direction  in  the  cyclone.  The  heat  liberated  by  the  conden- 
sation of  the  aqueous  vapor  of  the  atmosphere  would  keep  up  the 
vertical  convection,  and  the  discharge  of  the  atmosphere  from  the 
upper  end  of  the  vortex  tube  would  be  largely  instrumental  in 
building  up  the  areas  of  high  pressure  or  anti-cyclonic  areas,  which 
are  always  found  to  be  developed  in  connection  with  centres  of 
low  pressure.  In  the  anticyclone  the  winds  circulate  in  a  clock- 
wise direction. 

The  above  is  substantially  the  outline  of  the  condensation 
theory  of  cyclones  as  given  by  Prof.  Ferrel.  There  has  been  an 
increasing  tendency  in  recent  years  among  meteorologists  to  the 
belief  that  the  theory  was  not  sufficient  to  explain  the  observed 
phenomena.  Some  have  thought  it  might  apply  to  tropical,  oceanic 
cyclones  or  others  developed  under  certain  conditions,  but  nearly 
all  have  agreed  that  there  have  been  many  other  cyclonic  storms 
which  could  not  be  explained  by  it. 

There  are  two  readily  understood  physical  difficulties  which 
limit  the  general  application  of  the  theory. 

1st.  The  theory  assumes  that  the  source  of  energy  of  the 
cyclone  is  mainly  in  the  heat  from  aqueous  condensation.  But 
there  have  been  many  well-developed  cyclones,  lasting  several  days, 
and  travelling  from  one  to  two  thousand  miles  with  little  or  no 
condensation.  Such  often  occur. 

2d.  The  isotherms  usually  trend,  in  the  United  States,  across 
the  cyclones  instead  of  running  circularly  about  the  centre  as  re- 
quired by  the  condensation  theory. 

From  a  thorough  study  of  cloud  observations  recently  made  in 
the  United  States  a  theory  of  cyclones  has  been  proposed  by  Prof. 
Bigelow,  of  the  U.  S.  weather  service,  which  unquestionably  seems 
to  be  more  in  accord  with  observed  facts. 

Under  this  idea  the  counter-currents  from  the  north  and  south, 
whose  circulation  is  established  from  cloud  observations,  and  to 
which  we  have  already  referred  as  accomplishing  the  interchange 
of  air  between  high  and  low  latitudes,  are  the  cause  of  the  cyclonic 
circulation  over  the  United  States.  These  counter-currents,  it 
will  be  remembered,  flow  in  the  strata  below  the  three-mile  level, 
their  level  of  greatest  activity  being  at  about  one  and  a  half  to  two 
miles;  they  have  different  velocities  at  different  altitudes,  and  de- 


146 


ELEMENTARY  LESSONS  IN  HEAT. 


pend  for  their  motion  upon  pressure  gradients  extending  far  to  the 
north  and  south.  These  thin  streams  from  different  directions 
pass  alternately  over  the  same  areas,  and  by  their  interaction  upon 
each  other  cause  the  phenomena  of  anticyclones  and  cyclones.  It 
is  attempted  to  convey  an  idea  of  the  suggested  interaction  in 
Fig.  54. 

NORTH 


SOUTH 
FIG.  54.    (After  BIOKLOW.) 


In  the  case  under  consideration,  the  currents  coming  from 
opposite  directions,  north  and  south,  have  the  contiguous  edges  of 
adjacent  streams  deflected  by  the  earth's  rotation  in  opposite  direc- 
tions, thus  tending  to  produce  alternate  areas  of  high  and  low 
pressure.  In  the  highs  the  air  is  driven  toward  the  ground,  and  in 
the  lows  it  ascends  by  mechanical  vortex  motion. 

The  ascensional  currents  of  the  low  areas  are  fed  partly  by  the 
outflowing  air  from  the  high  areas  and  partly  from  the  outer 
branches  of  the  currents  which  produce  the  highs. 

The  gyratory  action  produced  is  attributed  to  the  meeting  of 
currents  at  an  angle,  with  the  development  of  the  couple  effect 
which  gives  the  circular  adjustment  common  in  fluid  motions.  A 
single  current  flowing  obliquely  over  a  mountain  range  or  follow- 
ing a  coast  line  of  changing  direction  continually  tends  to  run  into 
this  same  motion. 

The  gyrations  are  most  strongly  developed  at  the  height  of 
about  1.5  miles  in  both  cyclones  and  anticyclones,  and  the  observa- 
tions show  that  the  effects  of  the  anticyclonic  motions  of  the  high 


AERIAL  AND  AQUEOUS  METEORS.  147 

areas  extend  to  a  much  greater  altitude  than  the  cyclonic  motions 
of  the  low  areas.  We  cannot,  therefore,  avoid  the  conclusion  that 
the  high  areas  are  the  dominant  and  the  low  areas  the  subordinate 
features  in  the  circulation.  The  anticyclones  draw  from  and  the 
cyclones  discharge  into  the  upper  atmosphere,  both  being  produced 
by  the  interaction  of  currents  from  opposite  directions,  which 
themselves  have  their  sources  of  energy  at  long  distances  from  the 
gyrating  mass.  The  motion  of  the  air  toward  the  axis  of  the 
cyclone  under  mechanical  laws  produces  the  ascensional  flow, 
instead  of  this  flow  drawing  in  the  air  as  the  couvectional  theory 
requires. 

It  is  true  that  the  ascent  and  cooling  of  the  air  by  contact  with 
colder  air  causes  condensation  of  the  aqueous  vapor,  and  the  liber- 
ated heat  thereof  increases  the  upward  motion.  The  mechanical 
causes  would  thus  be  assisted  to  varying  extent  by  the  heat  from 
condensation,  this  agent  being  especially  prominent  in  cyclones 
producing  heavy  rainfall.  The  heat,  no  doubt,  in  some  cases,  is  a 
very  important  factor  in  producing  the  convectional  current. 

We  therefore  trace  back  the  principal  propelling  energy  of  the 
cyclones  and  anticyclones  to  the  general  circulation.  This  energy 
is  stored  in  horizontal  convection  currents  flowing  from  north  and 
south;  these  currents  being  driven  by  gradients  produced  by  the 
general  circulation  and  often  extending  long  distances  from  the 
storm  gyrations.  Half  the  mass  of  the  atmosphere  is  below  the  three- 
mile  level,  and  it  is  in  this  mass  that  temperature  changes  mainly 
occur.  In  this  mass  the  north  and  south  currents  flow,  effecting 
an  interchange  between  northern  and  southern  regions,  while  the 
anticyclonic  and  cyclonic  motions  cause  interchange  in  a  vertical 
direction.  Above  the  three-mile  level  there  is  little  interchange  in 
meridianal  direction  and  the  general  drift  of  the  air  is  eastward. 
This  upward  and  downward  interchange  by  gyrating  columns  con- 
nects the  lower  mass  of  air  with  the  upper,  and  the  general  motion 
of  the  former  is  thus  influenced  by  the  eastward  trend  of  the  latter. 

The  planetary  circulation  as  modified  by  the  continental  dis- 
tribution of  land  and  water,  coupled  with  the  relative  temperature 
gradients  which  exist  over  these  in  summer  and  winter,  establishes 
the  interchanging  currents  which  flow  from  north  to  south  over 
our  continent.  The  causes  named  tend  to  build  up  a  permanent 
high  area  over  the  north  and  extreme  northwest  part  of  the  conti- 


148 


ELEMENTARY  LESSONS  IN  HEAT. 


nent  iu  winter,  from  which  currents  of  cold  air  flow  to  the  south. 
The  heat  energy  of  the  tropics. expends  itself  in  driving  currents  to 
the  north.  These  currents  by  their  interactions  produce  the  high 
and  low  areas  which  sweep  over  the  United  States,  the  high  areas 
being  the  dominant  and  the  low  areas  the  subordinate  features  ; 
the  cyclones  being  mainly  operated  by  the  outflow  from  the  anti- 
cyclones, and  their  motion  being  dependent  upon  the  motion  and 
location  of  the  latter.  Northern  and  southern  currents,  bearing 
the  temperatures  of  the  regions  from  which  they  come,  produce, 


FIG.  55.    (After  BIGELOW.) 

respectively,  our  cold  and  warm  waves.  Fig.  55  illustrates  the 
relation  of  a  high  and  a  low  in  a  storm  covering  the  central 
valleys. 

Progressive  Motion  of  Cyclones. — Besides  the  motion  of  the 
winds  in  the  cyclone,  the  cyclone  itself  moves  from  one  region  to 
another,  and  with  few  exceptions  the  progression  is  eastward  or 
northeastward.  Several  causes  are  thought  to  be  active  in  produc- 
ing this  motion  of  translation. 

1st.  Probably  the  most  important  factor  is  the  eastward  motion 
of  the  higher  air  into  which  the  gyrating  columns  of  the  cyclones 
extend  ;  they  are  thus  drawn  along  by  the  upper  air  of  the  general 


AERIAL  AND  AQUEOUS  METEORS.  149 

circulation.  The  centrifugal  force  of  the  rotating  winds  is  in  the 
direction  of  the  upper  circulation  on  the  east  side  of  the  cyclone 
and  opposed  to  it  on  the  west  ;  this  condition  facilitates  the  ascent 
of  the  air,  or  prevents  stagnation  on  that  side  and  tends  to  transfer 
the  centre  in  that  direction. 

2d.  The  winds  which  feed  the  cyclone  are  of  unequal  absolute 
humidity.  Those  most  heavily  laden  with  moisture  produce  the 
greater  condensation  when  they  enter  the  ascending  column  of  the 
cyclone  and  thus  produce  a  section  of  greater  precipitation,  and, 
more  heat  being  produced  in  this  section,  the  tendency  is  to  trans- 
fer the  storm  centre  to  that  side. 

3d.  The  earth's  rotation  also  is  a  factor  in  determining  the 
progress.  The  deflective  force  due  to  this  rotation  increases  with 
the  latitude,  and,  since  the  cyclones  are  often  of  great  extent,  the 
difference  of  its  action  on  the  north  and  south  sides  of  the  cyclone 
has  an  influence.  This  force  acts  with  the  centrifugal  force,  due 
to  the  gyrations  of  the  air,  to  transfer  the  centre  of  the  cyclone 
toward  the  side  of  greatest  deflection. 

4th.  The  areas  surrounding  the  cyclone  will  not  all  be  at  the 
same  pressure.  The  strongest  winds  will  blow  from  the  area  of 
greatest  pressure.  As  these  winds  curve  around  the  vortex  of  the 
cyclone  they  will  resist  being  drawn  inward  more  powerfully  than 
the  weaker  winds,  and  consequently  tend  to  draw  the  centre  of  the 
cyclone  toward  the  swiftest  part  of  the  revolving  disk. 

In  the  progressive  motion  of  the  cyclone  there  is  not  a  contin- 
uous transfer  of  the  same  gyrating  mass  of  air  to  widely  different 
places,  but  the  progression  takes  place  by  the  continual  forming  of 
a  new  cyclone  in  the  line  of  advance,  which  line  is  determined  by 
causes  already  given.  New  masses  of  air  are  thus  continually 
brought  into  the  movement,  while  the  gyrations  of  that  in  the  rear 
are  destroyed  by  friction.  Since  the  winds  are  travelling  in  nearly 
opposite  directions  on  opposite  sides  of  the  cyclone,  the  progressive 
motion  of  the  cyclone  will  evidently  carry  these  opposite  winds  over 
any  places  properly  situated  ;  hence  this  progressive  motion  gives 
also  an  explanation  of  the  veering  of  winds  during  the  storm. 

Paths  of  Cyclones. — The  paths  of  cyclones  are  the  lines  travelled 
by  their  centres,  and  with  few  exceptions  their  directions  are  to  the 
eastward.  In  the  United  States  .the  average  direction  of  motion, 
as  given  by  Prof.  Loomis;  is  nine  degrees  north  of  east,  with  an 


150  ELEMENTARY  LEkSONS  IN  IIKAT. 

average  of  twenty-eight  and  four-tenths  miles  per  hour.  In  the 
United  States  the  valley  of  the  St.  Lawrence  is  the  line  most  fre- 
quently swept  by  cyclones.  The  areas  of  low  barometer  are  not 
circular  but  elliptical ;  the  average  ratio  of  the  axes  is  about  1.5. 
The  average  direction  of  the  longer  axis  of  the  storm  is  N.  36°  E. 

In  Fig.  56  is  shown  by  full  barbed  lines  the  approximate  place 
of  origin  and  the  average  line  of  travel  of  all  the  storms  that  passed 
over  the  United  States  from  1884  to  1893.  The  number  travelling 


FIG.  56.    (After  BIGELOW.) 

each  route  is  indicated.  It  is  seen  that  all  leave  the  country  by 
way  of  New  England,  and  the  greater  number  originate  in  Alberta. 

When  a  cyclone  at  sea  reaches  a  low,  level  coast,  the  combined 
effect  of  the  diminished  pressure  and  the  strong  winds,  especially 
if  the  tides  also  act  in  conjunction,  may  carry  a  destructive  wave 
over  the  land.  Such  waves  have  wrought  immense  destruction 
over  the  lower  delta  of  the  Ganges  and  along  our  Texas  coast. 

Low-area  Storms. — In  the  foregoing  discussion  the  term  cyclone 
has  been  used  to  include  all  large  storms  involving  the  cyclonic 
motion,  and  low-area  storms  are  properly  included.  The  custom 
of  the  United  States  Signal  Office  and  the  public  press  has, 
however,  to  a  certain  extent  created  a  popular  distinction  between 


AERIAL  AND  AQUEOUS  METEORS.  151 

low-area  storms  and  cyclones.  By  the  limitations  thus  imposed, 
the  term  cyclone  is  generally  restricted  to  certain  tropical  storms 
that  usually  have  a  parabolic  path  extending  westward  and  north- 
ward from  their  point  of  origin  off  the  west  coast  of  Africa,  near 
the  doldrums,  to  about  the  30th  parallel  and  the  70th  meridian. 
At  this  point  the  vertex  of  the  parabola  is  reached,  and  the  storm 
progresses  to  the  northeastward  parallel  to  the  coast  of  the  United 
States.  These  storms  have  a  great  power  of  continuance,  and 
usually  expand  as  they  go.  They  sometimes  extend  their  west- 
ward course  to  and  beyond  the  United  States  coast,  and  then  the 
northern  branch  of  the  path  passes  over  the  land,  producing  some 
of  our  most  violent  storms. 

The  low-area  storms,  under  the  above  distinction,  are  those 
cyclonic  storms  that  originate  in  the  interior  of  our  country  and 
run  their  courses  as  modified  by  the  causes  already  given. 

The  low-area  storms  are  cyclonic,  but  the  term  cyclone,  in 
popular  use,  is  applied  to  those  just  mentioned  or  to  t)ie  very 
violent  of  the  low-area  storms.  Such  real  distinction  as  exists  is 
based  upon  the  path  or  intensity  of  the  storm.  It  must  be  remem- 
bered that  the  term  cyclone,  as  here  used,  applies  to  all  cyclonic 
storms. 

The  progressive  motion  of  the  severe  tropical  cyclones  just 
referred  to  is  probably  explained  by  the  location  of  the  high  area 
in  the  North  Atlantic,  the  cyclone  being  fed  by  and  rotating  along 
the  edge  of  the  high  area.  The  motion  of  the  trade  winds  and  th<s 
great  condensation  which  accompanies  these  storms  are  also  proba- 
bly important  factors  in  their  propagation. 

Effects  of  the  Cyclone  and  Anticyclone  on  Normal  Temperature. 
— Since  the  gyratory  motions  of  the  winds  in  the  cyclone  in  the 
northern  hemisphere  are  always  from  right  to  left,  as  above  de- 
fined, the  colder  air  of  the  north  is  carried  around  to  the  west  side, 
while  the  warmer  air  of  the  south  is  brought  to  the  east  side  of  the 
cyclone.  The  motions  may  materially  affect  the  temperatures 
which  would  otherwise  exist,  especially  on  the  east  and  west  sides, 

Wherever  high  pressure  areas  exist,  the  tendency  is  for  the 
air  to  flow  out  beneath  and  to  inaugurate  more  or  less  perfectly  the 
conditions  of  a  cyclone  with  a  cold  centre,  or  what  is  more  gener- 
ally designated  an  anticyclone. 

It  has  been  shown  in  such  cases  that  there  are  descending  in- 


152  ELEMENTARY  LKS80N8  IN  HEAT. 

stead  of  ascending  currents,  and  under  such  conditions  there  could 
be  no  condensation;  hence  a  high  barometer  usually  brings  or  ac- 
companies a  clear  and  dry  atmosphere.  As  radiation  and  evapo- 
ration take  place  much  more  readily  under  such  conditions,  the 
weather  with  high  barometer  is  likely  to  be  cooler  also.  These 
principles,  coupled  with  the  fact  that  the  highs  often  draw  air 
from  great  altitudes,  are  sufficient  to  explain  the  cooler  and  clearer 
weather  which  usually  accompanies  the  high  barometer. 

Tornadoes. — Tornadoes  are  small  violent  cyclones.  They  ex- 
tend over  an  area  too  small  to  be  affected  by  the  earth's  rotation, 
yet  they  all  in  the  northern  hemisphere  revolve  from  right  to  left 
(opposite  to  the  hands  of  a  watch  with  face  up),  and  probably 
derive  their  gyrations  from  the  motions  of  the  air  in  which  they 
originate.  While  the  cyclone  of  considerable  extent  may  be  com- 
pared to  a  revolving  disk  of  a  diameter  many  times  its  depth,  the 
tornado  is  a  tall  column  of  gyrating  air  whose  height  is  many  times 
its  diameter.  In  the  cyclone,  therefore,  the  gyrations  are  much 
retarded  by  friction  against  the  earth,  and  in  the  tornado  the  gyratory 
velocity,  except  in  the  lower  strata,  which  are  in  contact  with  the 
earth,  is  very  nearly  in  accordance  with  the  law  of  central  forces, 
varying  inversely  as  the  distance  from  the  centre.  On  account  of 
this  rapid  gyration,  the  effects  produced  in  the  cyclone  are  here 
intensified,  and  the  gyrations  a  short  distance  above  the  surface  are 
nearly  circular,  and  the  centrifugal  force  of  the  gyrations  here 
tends  to  produce  a  vacuous  column  into  which  the  air  cannot  enter 
from  the  sides.  There  is,  therefore,  a  great  diminution  of  pressure 
within,  and  especially  at  the  centre  of  this  column.  The  gyratory 
motion  of  the  lower  air  only  is  much  diminished  by  friction  against 
the  earth ;  it  therefore  flows  toward  the  centre  of  low  pressure  and 
ascends  with  great  velocity. 

These  indrawn  currents  are  the  most  destructive  ones,  and  are 
so  strong  that  they  sweep  along  and  carry  up  heavy  bodies  and  at 
times  transport  them  long  distances.  The  black  funnel-shaped 
clouds  which  accompany  the  cyclone  are  due  to  the  condensation 
of  the  moisture  of  the  ascending  air.  The  pressure  of  the  air  at 
and  near  the  centre  of  the  tornado  is  so  greatly  diminished  that 
the  stratum  of  condensation  and  cloud-formation  is  frequently  there 
brought  down  (or  nearly  so)  to  the  earth's  surface.  As  we  depart 
from  the  centre  of  the  tornado  the  pressure  is  not  so  greatly  dimin- 


AERIAL  AND  AQUEOUS  METEORS.  153 

ished  and  the  point  of  condensation  is  not  so  low,  so  that  the  base 
of  the  funnel-shaped  cloud  is  above.  The  depending  point  is 
sometimes  seen  to  withdraw  into  the  cloud-mass  above  and  to  sud- 
denly dart  forth  again.  These  effects  are  due  simply  to  variations 
in  the  level  at  which  condensation  takes  place,  depending  upon 
varying  pressure,  and  this  level  may  descend  more  rapidly  than  the 
air  ascends,  so  that  the  vapor  column  shoots  from  above  downward, 
while  the  air  in  which  the  condensation  takes  place  is  all  the  time 
moving  upward.  The  diminution  of  pressure  in  violent  tornadoes 
is  very  great,  sometimes  amounting  to  three  inches  of  the  baro- 
metric column.  When  such  a  tornado  comes  suddenly  over  a 
building,  or  otl^er  confined  space,  such  as  a  cellar,  from  which  the 
air  at  ordinary  pressure  cannot  readily  escape,  there  is  exerted  a 
great  pressure  from  within  outward.  From  this  cause  the  explo- 
sions occur  which  unroof  buildings  and  throw  their  walls  outward, 
burst  open  cellar-doors  against  a  strong  direct  wind,  etc. 

The  average  width  of  the  path  of  destruction,  as  given  by  Fin- 
ley  from  a  large  number  observed,  was  about  a  thousand  feet. 
Tornadoes  generally  accompany  cyclones,  and  Finley  has  shown 
that  they  occupy  pretty  constant  positions  with  reference  to  the 
centre  of  the  cyclones.  The  greatest  number  of  tornadoes  occur, 
in  this  country,  in  the  States  of  Kansas,  Missouri,  and  Illinois,  and 
they  are  most  frequent  in  the  month  of  June. 

The  phenomenon  of  a  tornado  is  probably  due  to  horizontal 
counter-currents,  more  local  but  similar  to  those  which  produce 
cyclones,  flowing  above  an  unstable  atmosphere.  These  currents 
by  their  interactions  develop  gyrations  which  are  doubtless  greatly 
increased  by  the  vertical  convection  of  a  moist  unstable  atmos- 
phere, producing  a  vortex  tube  of  great  rotational  velocity. 

Water-spouts* — These  are  but  special  cases  of  tornadoes  which 
pass  over  bodies  of  water,  and  in  which  the  dependent  portion  of 
the  accompanying  cloud  is  reduced  to  a  long  slender  stem  extend- 
ing down  to  the  water.  Owing  to  the  diminished  pressure  at  the 
centre  of  the  tornado,  the  water  beneath  rises  up  into  a  mound,  is 
lashed  into  foam,  and  large  quantities  of  it  are  carried  aloft  by  the 


*  These  phenomena  might  with  equal  propriety  come  in  the  next  chapter 
where  results  are  considered,  but  when  causes  are  considered  their  explanation 
follows  more  naturally  here. 


154  ELEMENT AET  LESSONS  IN  HEAT. 

ascending  currents  of  air.  From  small  lakes  and  ponds  the  inhab- 
itants thereof  may  be  carried  aloft  with  the  water  and  descend  at 
considerable  distances,  giving  showers  of  fish,  frogs,  etc. 

Cloud-bursts.* — By  the  ascending  and  gyrating  currents  of  air 
in  a  tornado,  a  great  quantity  of  rain  or  condensed  moisture  may 
be  carried  along  until  its  weight  becomes  so  great  that  it  descends 
in  streams,  or  until  the  tornado  has  its  force  broken  by  some  mate- 
rial object,  such  as  a  crag  or  peak,  when  the  accumulated  rain  de- 
scends almost  in  a  mass,  with  terrific  effect. 

*  See  foot-note  on  preceding  page. 


OHAPTEK    XL 

AQUEOUS   METEORS. 

UNDER  this  head  are  included  all  the  visible  phenomena  which 
result  from  the  condensation  of  the  aqueous  vapor  in  the  atmos- 
phere, and  this  condensation  always  occurs  whenever  the  tempera- 
ture of  the  air,  from  any  cause,  falls  below  the  dew-point.  The 
most  commonly  observed  of  such  phenomena  will  be  described. 

Mists,  Fogs,  and  Clouds. — These  result  whenever  the  aqueous 
vapor  of  the  atmosphere  is  condensed  and  suspended  in  visible 
form.  This  condensed  vapor  is  believed  to  exist  as  liquid  particles 
or  spheres,  not  hollow,  differing  from  rain-drops  only  in  size. 
Their  suspension  is  due  to  the  viscosity  of  the  air  and  to  the  fact 
that  the  atmosphere  is  never  absolutely  quiescent,  and  the  vapor 
particles  are  kept  floating  like  dust  and  other  solid  particles  which 
are  often  observed  in  the  air  and  which  are  seen  never  to  be  at 
rest. 

Fogs  and  Mists. — Fogs  and  mists  differ  from  clouds  merely  in 
that  they  are  formed  at  less  elevation.  They  are  due  to  local 
causes,  and  may  be  formed  in  several  ways.  At  the  first  approach 
of  winter,  when  the  air  of  a  region  is  often  many  degrees  colder 
than  the  water,  mists  are  seen  to  overspread  the  streams,  the  vapor 
arising  from  them  being  condensed  by  the  cold  air.  The  same 
phenomenon  is  often  observed  when  the  conditions  are  reversed,— 
when  the  water  is  colder  than  the  air. 

Fogs  are  often  formed  at  night  or  late  in  the  day,  at  the  lowest 
lines  of  valleys  and  in  depressed  areas,  while  the  sides  of  the  valley 
and  knolls,  though  of  but  slight  elevation,  especially  if  covered 
with  vegetation,  are  exempt  from  them.  This  results  from  the 
presence  of  more  moisture  in  the  open  valley  and  the  more  rapid 

155 


156  ELEMENTARY  LESSONS  IN  HEAT. 

radiation  as  compared  to  wooded  areas,  and  also  sometimes  partly 
from  the  fact  that  the  air  which  is  cooled  at  the  higher  levels,  if 
there  are  no  winds,  descends  to  the  lower.  Sheep  and  other  animals 
learn  to  take  advantage  of  these  natural  conditions,  and  are  often 
seen,  in  the  early  morning,  to  have  spent  the  iiight  just  above  the 
damper  atmosphere.  In  the  elevated  regions  of  our  western  coun- 
try, among  the  narrow  valleys  of  the  Sierras  and  the  Rocky  Moun- 
tains, quite  marked  climatic  effects  result  from  these  causes  alone. 
In  those  regions  nourishing  gardens  are  often  seen  situated  near  the 
forest  growth  at  the  sides  of  the  valley,  while  nearer  the  axis  of 
the  valley  and  not  over  five  miles  away,  and  two  hundred  feet 
lower,  many  of  the  same  vegetables  cannot  be  successfully  grown. 
Again,  orchards  well  up  on  the  side  slopes  are  productive,  while 
lower  down  the  valley  they  are  comparative  failures. 

As  a  further  illustration  of  these  principles  the  following  in- 
stance may  be  cited.  In  September,  1877,  while  engaged  in  survey 
work  in  the  Sierras  of  Northern  California,  for  the  purpose  of  being 
early  on  the  summit  of  a  mountain  the  author  spent  the  night  far 
up  the  side,  some  two  thousand  feet  above  the  camp  of  the  party 
in  the  valley  below,  though  within  sight.  Before  sunrise  the  next 
morning  the  difference  of  temperature  between  the  two  stations  at 
the  same  hour  was  7°  F.,  the  upper  being  the  warmer.  The  night 
was  very  clear  and  still.  Eecent  investigations  show  that  the  air 
at  higher  altitudes  is,  at  night,  often  warmer  than  that  lower  down 
— an  inversion  of  the  ordinary  relations. 

As  low-lying  fogs  are  usually  accompanied  by  more  or  less 
dew,  a  knowledge  of  their  origin  is  an  important  aid  to  the  selection 
of  the  best  camping  sites  where  there  are  no  other  considerations. 
From  the  illustrations  given,  it  will  be  seen  that  the  most  favorable 
sites,  where  it  is  desirable  to  avoid  dampness  and  cold,  are  those 
protected  from  direct  radiation,  some  distance  above  the  lowest 
neighboring  levels,  and  upon  a  ridge  rather  than  a  ravine  leading 
to  these  levels.  If  not  within  the  timber,  it  will  be  well  to  have 
the  latter  on  the  slope  above  rather  than  to  camp  upon  an  open 
hillside. 

Clouds. — There  are  several  kinds  of  clouds,  and  they  shade  into 
each  other,  so  that  there  can  be  no  precise  classification.  "We  shall 
refer  only  to  the  four  principal  classes. 


AQUEOUS  METEORS.  157 

Cumulus. — These  are  the  rounded  masses  or  convex  heaps  ex- 
tending upward  from  flat  horizontal  bases.  They  are  very  common 
in  summer,  and  are  believed  to  be  due  to  the  condensation  of 
ascending  columns  of  vapor.  The  flat  base  marks  the  level  where 
condensation  begins,  and  the  rounded  masses  are  the  tops  of  the 
ascending  columns.  If  the  cumulus  is  overhead,  its  typical  form 
cannot  be  seen,  and  it  will  not  be  observed  as  such.  These  clouds 
are  consequently  noticed  only  on  the  horizon. 

Stratus. — These  consist  of  horizontal  layers,  and  are  generally 
at  low  levels.  They  are  probably  due  to  the  cooling  of  a  compara- 
tively still  atmosphere  by  radiation  ;  when  the  dew-point  is  reached 
at  a  certain  level,  the  first  layer  is  formed.  These  clouds  may  result 
from  a  fog  lifted  in  a  horizontal  stratum.  They  frequently  appear 
at  sunset  and  disappear  in  the  morning. 

Prof.  Bigelow  has  concluded  from  cloud  observations  that 
stratus  clouds  are  often  produced  as  sheets  at  the  contact  surface 
of  the  streams  of  air  at  different  temperatures  and  altitudes  flowing 
past  each  other,  the  upper  having  the  greater  velocity.  The  cu- 
mulus may  be  produced  at  different  levels  by  vertical  ascension  of 
columns  in  strata  having  the  same  velocity  throughout. 

Cirrus. — These  clouds  are  of  great  variety,  but  the  most  char- 
acteristic are  the  fibrous,  feathery  clouds  which  float  in  the  higher 
atmosphere.  It  is  to  these  clouds  that  halos  are  due,  and  such 
clouds  are  believed  to  be  often  composed  of  particles  of  ice. 

Nimbus  is  any  cloud  from  which  rain  is  falling. 

The  classification  of  clouds  is  further  differentiated  into  other 
types  quite  distinct,  though  grading  into  the  classes  given;  as  cirro- 
stratus,  cirro-cumulus,  alto-stratus,  strato-cumulus,  cumulo-nimbus. 

Altitude  and  TJiickness  of  Clouds. — Clouds  are  formed  at 
various  heights,  from  near  the  surface  of  the  earth  up  to  at  least 
ten  miles.  Stratus  and  cumulus  are  the  lowest,  cirrus  the  highest, 
and  composite  clouds  intermediate.  Several  cloud  masses  often 
overlie  one  another  with  clear  space  between.  This  arrangement 
has  been  observed  in  balloon  ascents. 

Cloud  Shadows. — In  a  hazy  atmosphere  the  shadows  of  clouds 
are  frequently  distinctly  shown  by  dark  lines  proceeding  from  the 
sun.  When  these  lines  of  light  and  shadow  extend  downward  and 
toward  rivers  or  other  bodies  of  w^ater,  the  sun  is  popularly  said  to 
be  "  drawing  water."  The  same  effect  is  frequently  seen  just  before 


158  ELEMENTARY  LESSONS  IN  HEAT. 

and  after  sunset  and  also  at  sunrise,  being  a  conspicuous  feature  of 
morning  and  evening  twilight. 

Cloud  Formation. — Clouds  may  result  from  reduction  of  tem- 
perature due  to  loss  of  heat  by  the  air, — 

(1)  From  direct  radiation  into  the  upper  space. 

(2)  From  proximity  to  colder  masses,  such  as  ice-fields  or  moun- 
tain-tops. 

(3)  From  expansion  due  to  diminished  pressure,  as  when  the 
air  from  any  cause  is  made  to  ascend. 

(4)  From  cooling  by  contact  in  the  partial  or  complete  mixture 
of  two  masses  of  air  at  different  temperatures. 

Rain. — When  the  condensation  of  the  aqueous  vapor  takes  place 
with  such  rapidity  that  the  liquid  particles  enlarge  and  fall  to  the 
earth  in  drops,  we  havo  the  phenomenon  of  rain.  The  causes 
which  produce  clouds  tend  also  to  produce  rain,  but  only  the  third 
and  fourth  of  the  above  causes  are  sufficient;  the  others  are  believed 
never  to  result  in  rain. 

Any  of  the  agencies,  then,  which  cause  a  sufficient  ascent  of 
moist  air  will  produce  rain.  The  most  evident  illustration  of  this 
fact  is  seen  wherever  vapor-bearing  winds  blow  over  high  moun- 
tains. The  trade-winds  deflected  upward  by  the  Andes  give  the 
heavy  rainfalls  at  the  head-waters  of  the  Amazon.  The  coast 
ranges  of  Washington  and  Oregon,  lifting  up  the  prevailing  winds 
from  the  Pacific,  give  the  heavy  rains  of  that  region.  The  greatest 
average  rainfall  of  the  known  world  is  at  Chirra  Poongee,  in  the 
Cassya  Mountains,  about  three  hundred  miles  north  of  the  head  of 
the  Bay  of  Bengal.  The  rainfall  at  this  place,  according  to  Gen- 
eral Greely,  has  averaged  493.2  inches  per  year  since  1871;  in  1861 
there  is  said  to  have  fallen  there  the  enormous  amount  of  905.1 
inches.  The  cause  of  this  heavy  fall  is  the  passage  of  the  winds 
of  the  Indian  monsoon  over  the  lofty  ranges  which  are  part  of 
the  Himalaya  system. 

It  is  not  believed  that  currents  of  air  ever  mingle  with  sufficient 
rapidity  to  produce  rain,  but  it  is  probable  that  a  moisture-bearing 
stratum  may  be  lifted  upward  by  the  intrusion  of  a  colder,  denser 
layer  below,  and  thus  produce  rain.  When  such  an  atmospheric 
wedge  protrudes  from  the  north  over  the  eastern  part  of  the  United 
States,  especially  in  mild  winter  weather,  we  have,  according  to 


AQUEOUS  METEORS.  159 

Prof.  Ferrel,  an  explanation  of  the  drizzly  weather  with  a  north- 
northeast  wind,  sometimes  lasting  for  several  days.  At  other 
times  such  conditions  give  the  cold  waves  already  mentioned. 

Cyclonic  Rains. — These  are  the  rains  which  accompany  the 
great  cyclonic  or  low-area  storms  already  mentioned,  and  are  the 
usual  rains  which  prevail  in  this  country  east  of  the  great  plains. 
They  are  due  to  the  ascent  of  the  air  in  the  cyclones  as  already 
described,  and  to  the  direct  cooling  of  the  moist  warm  air  by  con- 
tact with  the  cold  air  as  the  two  winds  are  drawn  into  thin  spiral 
filaments  in  their  motion  around  the  cyclonic  centre. 

In  many  of  our  cyclonic  rain-storms  the  condensation  produced 
by  the  ascension  of  the  air  in  the  cyclone  is  added  to  by  the  fact 
that  the  moisture-bearing  winds  from  the  sea  move  over  a  cold  land 
at  the  same  time  that  they  are  travelling  northward.  In  other  words, 
causes  2,  3,  and  4  above  given  are  united  in  the  cyclonic  storms. 

The  observations  of  these  rain  areas  show  them  to  be  generally 
of  an  elliptical  form,  as  is  the  case  with  isobars  *  of  the  cyclone, 
but  the  rain  areas  coincide  only  roughly  and  in  a  general  way  with 
the  areas  of  barometric  depression,  for  the  condensed  vapor  is  gen- 
erally, in  part  at  least,  carried  beyond  the  low  area  by  the  outflow- 
ing air  before  it  can  fall  as  rain.  From  Prof.  Loomis's  extended 
studies,  these  areas  are  seen  to  approximate  to  an  ellipse,  the  major 
axis  of  which  is  about  twice  as  long  as  the  minor,  the  lesser  axis 
frequently  being  more  than  five  hundred  miles  long.  North  of  36° 
the  average  distance  of  the  centre  of  the  greatest  rainfall  from  the 
centre  of  low  pressure  is  about  four  hundred  miles,  and  at  times 
the  distance  is  nearly  twice  as  great.  The  direction  of  the  longer 
axis  of  the  rain  area  and  the  direction  of  the  centre  of  greatest 
rainfall  from  the  centre  of  low  pressure  are  generally  the  same  aa 
the  direction  of  the  path  of  the  cyclone. 

Although  rains  usually  accompany  cyclonic  storms,  some,  as  al- 
ready stated,  have  been  observed  without  them.  On  the  other  hand, 
while  rain  areas  are  usually  areas  of  low  barometer,  it  is  not  always 
so.  Rains  may  occur  without  sensible  depression  of  the  barometer. 
If  the  whole  atmosphere  of  an  extended  region  is  nearly  saturated 
and  near  to  the  unstable  condition,  local  causes  may  give  rise  to  as- 
cending currents,  with  the  production  of  clouds  and  rain  without 
sensible  depression  of  the  barometer.  Such  an  atmosphere  in  pass- 

*  Isobars  are  lines  drawn  on  a  map  through  points  at  which  the  barometric 
pressure  is  the  same. 


160  ELEMENTARY  LESSONS  IN  HEAT. 

ing  over  the  land,  especially  during  warm  weather,  is  subjected  to  a 
variety  of  temperature  conditions  due  to  the  varying  nature  of  the 
earth's  surface,  and  is  likely  to  produce  showery  weather. 

Measurement  of  Rainfall. — This  measurement  is  made  by  deter- 
mining the  depth  in  inches  to  which  the  rain  which  falls  on  any  area 
would  cover  that  area.  The  time  for  which  this  record  is  kept 
determines  the  fall  for  that  period.  The  instrument  used  for 
determining  the  fall  is  called  a  rain-gauge,  and  may  consist  of  a 
plain  cylindrical  cup  or  any  other  vessel  from  which  the  depth  of 
water  which  falls  on  any  given  area  may  be  measured.  The  gauge 
should  be  so  placed  as  to  be  entirely  uninfluenced  by  other  bodies, 
in  a  large  open  space  with  the  upper  surface  a  foot  or  two  above 
the  ground. 

Rainfall  of  the  United  States. — The  rainfall  of  the  United 
States,  as  taken  from  the  excellent  chart  of  Prof.  Loomis,  may  be 
summarized  as  follows: 

Over  the  whole  area  east  of  the  hundredth  meridian  there  is 
less  than  50  inches  and  more  than  25,  excepting  South  Carolina, 
Georgia,  and  the  Gulf  States,  which  have  more  than  50  and  less 
t.ian  75.  Between  the  hundredth  and  hundred  and  twentieth 
meridian  less  than  25  and  more  than  10,  except  a  strip  about  two 
hundred  and  seventy-five  miles  wide  extending  from  Salt  Lake  to 
the  Gulf  of  California,  which  has  less  than  10  inches.  West  of  the 
hundred  and  twentieth  meridian  there  is  more  than  25  and  less 
than  50  inches,  except  in  Northern  Oregon  and  in  Washington 
Territory,  where  there  is  more  than  50  inches. 

Dry  Regions  of  the  Globe. — There  are  large  tracts  of  the  earth's 
surface  over  which  very  little  rain  falls.  This  is  due  partly  to  the 
localization  of  the  areas  in  the  interior  of  continents  or  on  the  lee- 
ward sides  of  mountains,  so  that  the  air  is  deprived  of  all  moisture 
before  reaching  them.  Such  are  the  Great  Desert  of  Sahara,  large 
portions  of  Arabia  and  Persia,  the  desert  of  Gobi  in  Asia,  Central 
Australia,  Western  South  America,  and  the  southern  portion  of 
our  own  country  between  the  Rocky  Mountains  and  the  Sierras. 
Besides  their  continental  location  some  of  these  areas  are  materially 
influenced  by  their  positions  with  reference  to  the  general  circula- 
tion of  the  air. 

It  has  been  seen  that  there  are  two  belts  of  high  barometer 
which  encircle  the  earth  near  the  tropics,  and  that  the  air  settling 
down  from  them  flows  outward  both  toward  the  poles  and  toward 


AQUEOUS  METEORS.  161 

the  equator,  the  latter  current  helping  to  form  the  trade-winds. 
With  descending  motion  and  direction  toward  a  warmer  region,  there 
would  be  no  tendency  to  condensation,  but  the  reverse.  Where 
the  regularity  of  the  trade-winds  is  not  interfered  with,  we  should 
expect  little  rainfall,  and  such  is  found  to  be  the  case  at  sea.  The 
same  influences  are  felt  to  a  certain  extent  over  the  land.  By  an 
inspection  of  a  map  it  will  be  seen  that  the  Desert  of  Sahara,  the 
dry  regions  of  Arabia,  Persia,  and  our  own  country  are  between 
the  fifteenth  and  fortieth  parallels  in  the  northern  hemisphere, 
while  the  dry  region  of  Southern  Africa,  of  Australia,  and  a  large 
part  of  that  of  South  America  are  between  the  same  parallels  in 
the  southern  hemisphere. 

Snow,  Sleet,  and  Hail. — Snow.— The  conditions  which  produce 
the  rain-storms  will  precipitate  snow  when  the  level  at  which  con- 
densation takes  place  is  at  a  sufficiently  low  temperature.  Where 
the  temperature  does  not  sink  below  32°  F,,  snow  cannot  form. 
It  is  believed  that  snow  is  formed  by  the  direct  passage  of  vapor 
into  the  solid  state,  the  minute  crystals  attaching  themselves  to- 
gether into  flakes.  More  than  a  thousand  different  forms  of  flakes 
have  been  observed,  most  of  them  being  of  great  delicacy  and 
beauty.  From  the  loose  texture  of  snow  and  because  of  the  air 
imprisoned  in  the  flakes,  it  is  an  extremely  good  non-conductor  of 
heat,  and  protects  the  earth's  surface  from  the  cold  due  to  its  own 
radiation. 

Sleet. — This  term  is  often  applied  to  small  imperfect  spheres  of 
snowy  ice,  frequently  mingled  with  rain,  which  sometimes  fall  to 
the  earth.  These  are  believed  to  be  due  to  the  partial  melting  of 
snow-flakes,  during  their  passage  through  strata  of  higher  temper- 
ature, and  subsequent  regelation. 

Hail. — In  the  gyratory  motions  which  constitute  cyclones  and 
tornadoes,  we  have  seen  that  there  is  sufficient  energy  developed 
in  the  former  to  carry  the  rain  up  and  outward  beyond  the  region 
of  ascending  currents  before  it  falls  to  the  earth;  in  the  tornadoes 
much  heavier  bodies  are  kept  aloft.  It  is  the  developement  of 
strong  ascending  currents  in  storms  which  explains  the  phenome- 
non of  hail  precipitation.  If  the  hail  be  no  larger  than  rain-drops, 
it  is  only  necessary  to  conceive  that  the  liquid  di*ops  were  carried 
up  into  a  freezing  temperature,  and  then  outward  until  the  ascend- 
ing currents  no  longer  supported  them,  when  they  fell  to  the  earth. 


162  ELEMENTARY  LESSONS  IN  HEAT. 

But  frequently  hailstones  have  fallen  that  were  very  large,  some 
as  much  as  five  inches  in  diameter,  and  weighing  nearly  two 
pounds.  These  largest  stones  frequently  have  a  bunch  of  snow  at 
the  centre,  and  are  made  up  of  alternate  concentric  layers  of  ice  and 
snow.  The  most  plausible  explanation  in  these  cases  is  probably 
that  of  Prof.  Ferrel,  which  may  be  briefly  outlined  as  follows :  The 
strong  ascending  currents  of  the  hail-storm  carry  the  rain-drops 
up  into  the  snow  region,  and  before  'they  freeze  they  moisten  the 
snow-flakes;  these  adhere,  forming  an  incipient  snow-ball.  This 
ball  is  then  carried  upward  and  out  from  the  vortex  of  the  storm 
and  begins  to  descend,  but  before  reaching  the  earth  it  is  drawn 
by  the  inblowing  currents  below  again  into  the  ascending  whirl 
and  carried  up  to  receive  another  coatin-g  of  snow  and  perhaps  sub- 
jected to  a  very  low  temperature.  Descending  again,  as  it  passes 
outward  from  above  it  passes  through  a  rain  region,  and,  owing  to 
its  reduced  temperature,  it  freezes  the  particles  with  which  it 
comes  in  contact  and  thus  receives  a  coating  of  ice.  It  may  be 
again  and  several  times  drawn  into  the  whirl,  and  repeat  the  cir- 
cuit until  it  grows,  by  the  alternate  layers  of  ice  and  snow,  too 
heavy  to  be  kept  up  and  falls  to  the  earth.  A  hail-storm  differs 
from  a  common  tornado  in  that  its  ascending  currents  are  suffi- 
ciently strong  to  carry  the  solid  particles  up  to  freezing  regions. 
Hail  usually  occurs  in  summer,  because  the  conditions  for  violent 
tornadoes  are  more  frequent  then,  and  because  the  freezing  altitude 
in  winter  is  so  low  that  the  necessary  rain  region  does  not  exist  be- 
low the  snow,  the  passage  through  which  gives  the  ice  layer. 

Dew. — The  deposition  of  dew  depends  upon  cooling  caused  by 
radiation.  As  soon  as  the  sun  passes  below  the  horizon,  the  radia- 
tion of  heat  from  the  dark  portion  of  the  earth's  surface  is  no 
longer  compensated  by  solar  rays,  and  it  is  steadily  reduced  in  tem- 
perature. The  air  immediately  above  has  its  temperature  reduced 
by  contact  with  the  cool  surface,  and,  if  this  reduction  reaches  the 
dew-point  of  the  air,  the  moisture  is  deposited,  and  gravity  and  the 
force  of  cohesion  collect  it  into  the  pearly  drops  which  sparkle  in 
the  morning  sun.  If  there  be  clouds,  foliage,  or  screens  of  any 
sort  that  partially  or  wholly  intercept  the  radiant  heat  and  return 
it  to  the  earth,  they  will  tend  to  and  may  prevent  the  formation  of 
dew  by  preventing  a  sufficient  reduction  of  temperature. 

Those  bodies,  such  as  grass,  leaves,  etc.,  which  radiate  heat  well 


AQUEOUS  METEORS.  163 

but  are  not  warmed  by  contact  with  the  earth,  collect  the  moisture 
more  readily  and  abundantly  than  equally  good  radiators,  such  as 
stone  and  metal,  when  in  contact  with  the  earth.  A  gentle  motion 
of  the  air  by  which  a  greater  amount  of  it  is  brought  into  contact 
with  the  cool  earth  favors  the  deposition  of  dew,  but  stronger  winds, 
which  continually  shift  the  air  before  any  of  it  is  reduced  in  tem- 
perature to  the  dew-point,  prevent  the  deposition.  The  air  itself 
does  not  radiate  heat  as  readily  as  the  bodies  named,  so  that  by  its 
own  radiation  the  air  does  not  cool  as  rapidly  as  by  contact  with 
the  earth  and  other  better  radiators.  The  deposition  of  moisture 
on  the  outside  of  a  glass  of  ice-water  or  other  cool  surface  when 
taken  into  a  warm  room  is  due  to  the  cooling  of  the  air  to  the  dew- 
point,  exactly  as  is  done  by  the  earth  at  night. 

The  result  of  this  is  that  there  is  frequently  a  difference  of  sev- 
eral degrees  in  temperature  between  the  earth's  surface  and  the 
air  a  few  feet  above.  Consideration  of  the  principles  here  enunci- 
ated is  of  great  practical  importance  in  determining  the  best  places 
for  selecting  camps  in  the  field. 

This  explanation  of  the  formation  of  dew  is  that  first  given  in 
1814  by  Dr.  Wells,  an  American  residing  at  the  time  in  London. 

In  1879  certain  observations  were  made  at  the  Massachusetts  Ag- 
ricultural Station  by  Prof.  Stockbridge  which  show  that  the  earth, 
when  dew  is  formed,  is  not  always  cooler  than  the  air  above  it,  and 
that  in  certain  cases  much  of  the  vapor  which  is  condensed  into 
dew  is  exhaled  from  the  warmer  earth  and  condensed  by  the  cooler 
air  above  instead  of  being  condensed  from  the  air  by  the  cooler 
earth.  Mr.  Aitken  of  Falkirk,  Scotland,  in  1886  and  subsequently, 
from  apparently  independent  experiments  of  his  own  came  to  the 
same  conclusion. 

This  idea  of  dew  forming  from  aqueous  vapor  escaping  from  the 
ground  into  the  colder  space  above  must  have  occurred  to  all  who 
have  observed  how  abundantly  dew  often  forms  on  the  under  side 
of  an  oil-cloth  blanket  or  garment  when  placed  upon  the  ground, 
when  it  would  seem  impossible  for  the  moisture  to  have  come  from 
the  air.  Further  observations  on  this  interesting  subject  may 
materially  modify  Wells's  general  explanation. 

Frost. — If  the  dew-point  of  the  air  be  below  the  freezing  point, 
the  vapor  will  be  condensed  as  ice  and  then  constitutes  hoar-frost. 
Deposited  dew  may  also  be  frozen,  and  thus  often  forms  part  of 
the  earth's  mantle  of  frost 


APPENDIX  I. 

PEOBLEMS. 


1.  What  temperature  on  the  Fahrenheit  scale  corresponds  to  12° 
C.  ?     3.9°  C.  ?  -  273°  C.  ?     164°  C.  ? 

2.  Convert  the  following  into  Centigrade  and  Reaumur  read- 
ings :  98°  F. ;  60°  F. ;  212°  F.;  0°  F.;  -  460°  F.;  -  40°  F. 

3.  Convert  the  following  into  Fahrenheit  and  Reaumur  readings : 
36.67°  C.;  —  140°  C.? 

4.  The  difference  of  temperature  between  summer  and  winter 
at  West  Point  is  often  90°  F.     What  would  be  the  range  by  a  cen- 
tigrade thermometer  ? 

5.  What  temperature  is  expressed  by  the  same  number  on  the 
two  scales,  Fahrenheit  and  Centigrade  ? 

6.  A  thermometer  has  both  scales  (F.  and  C.)  graduated  upon 
it;  the  sum  of  the  readings  is  74.     What  is  the  temperature  ? 

7.  The  three  scales  R.,  F.,  and  C.  are  graduated  upon  the  same 
thermometer  tube;  the  sum  of  the  readings  is  52.     What  is  the 
temperature  ? 

8.  An  iron  girder-bridge  is  ninety-two  feet  long  at  0°  C.     What 
is  the  variation  in  its  length  when  the  winter  temperature  reaches 
0°  F.,  and  the  summer  temperature  80°  F.?     The  linear  expansion 
of  iron  is  given,  page  15. 

9.  Taking  the  same  extremes  of  temperature  as  above,  what  is 
the  difference  in  length,  in  summer  and  winter,  of  the  steel  rails  on 
the  road  between  New  York  and  Albany.     The  distance  between 
the  two  cities  is  about  150  miles.     Coefficient  of  expansion  of  the 
rails  may  be  taken  as  .0000118  for  each  degree  C. 

10.  Given  100  cu.  ft.  of  air  at  15.5°  C.,  what  will  be  its  volume 

16o 


166  ELEMENTARY  LE880N8  IN  HEAT. 

if  the  temperature  be  raised  to  19.5°  0.,  external  pressure  remain- 
ing the  same  ? 

11.  170  cu.  in.  of  oxygen  are  measured  at  10°  C.     What  will  the 
volume  be  in  case  the  temperature  sink  to  0°  0.,  external  pressure 
remaining  constant  ? 

12.  A  gas  has  its  temperature  raised  from  15°  C.  to  50°  C.  under 
constant  external  pressure;  at  the  latter  temperature  it  measures 
15  litres.     What  was  the  initial  volume  ? 

13.  Given  300  cu.  ft.  of  hydrogen  at  150°  C.,  what  must  be  its 
temperature  in  order  that  its  volume  may  be  increased  to  400  cu. 
ft.  ?    At  what  temperature  will  its  volume  be  600  cu.  ft.  ?    External 
pressure  constant. 

14.  Given  100  cu.  ft.  of  nitrogen  at  273°  C.,  what  will  be  its 
volume  if  the  temperature  be  reduced  to  0°  C.,  the  external  pres- 
sure remaining  constant  ?   To  —  273°  C.  ?   What  will  be  its  volume 
if  the  temperature  be  raised  to  546°  C.? 

15.  Given  1000  en.  ft.  of  gas  at  60°  F.,  wliat  will  be  its  volume 
at  106°  F.,  the  external  pressure  remaining  constant  ? 

16.  Given  400   cu.   ft.   of   hydrogen   at  100°  F.,   required  its 
volume  at  200°  C. 

17.  Having  given  two  volumes  of  gas  of  40  and  60  cu.  ft.,  respec- 
tively, at  20°  C. ;   what  will  be  the  volumes  when  the  temperature 
falls  to  —10°  C.,  external  pressure  remaining  unchanged  ? 

18.  Prove  that  the  coefficients  of  expansion  2^-j  on  the  centi- 
grade scale  and  ^j^  on  the  F.  scale  represent  the  same  relative 
amounts. 

19.  If  the  bore  of  a  thermometer  tube  be  -^  of  an  inch  in  diam- 
eter, and  the  distance  between  the  freezing  and  boiling  points  on 
the  scale  be  six  inches,  what  is  the  capacity  of  the  bulb  and  the 
tube  below  the  freezing  point? 

20.  The  specific  gravity  of  absolute  alcohol  at  0°  C.  is  .793;  what 
is  it  at  25°  C.  ?     The  coefficient  of  expansion  of  alcohol  is  .001  for 
each  degree  C. 

21.  The  coefficient  of  cubical  expansion  of  mercury  is  .00018 
and  of  water  .0005  for  each  degree  C.     The  specific   gravity  of 
mercury  when  compared  with  water  at  20°  C.  is  13.568;  what  is  it 
when  compared  with  water  at  0°  C.? 

22.  A  flask  made  to  hold  ten  litres  is  filled  with  alcohol  at  10° 
G. ;  when  the  temperature  has  risen  to  30°  C.  how  much  alcohol 


PROBLEMS.  167 

will   overflow  ?      The   capacity  of  the   flask   is   not   supposed   to 
change. 

23.  *  5  Ibs.  silver  were  heated  to  160°  C.,  and  placed  in  25  Ibs. 
water  at  69°  C.,the  resulting  temperature  was  70°  0.     What  is  the 
specific  heat  of  silver? 

24.  30  Ibs.  sulphur  were  heated  to  100°  0.  and  placed  in  150 
Ibs.  water  at  10°  C.;  the  resulting  temperature  was  13.5°  0.    What 
is  the  specific  heat  of  sulphur  ? 

25.  Eequired  the  number  of  thermal  units  necessary  to  raise  the 
temperature  of  10  Ibs.  of  bismuth  from  0°  to  100°  C.     Sp.  ht.  of 
bismuth  =  0.03. 

26.  Eequired  the  number  of  thermal  units  necessary  to  raise  the 
temperature  of  5  Ibs.  dry  air  (at  constant  pressure)  from  0°  to  50° 
C.     Sp.  ht.  of  dry  air  (at  constant  pressure)  =  0.2375. 

27.  Given  10  Ibs.  ice  at  0°  C.,  and  100  Ibs.  water  at  13.4°  C. 
The  two  are  mixed,  and  when  all  the  ice  is  melted  the  temperature 
of  the  whole  is  5°  C.     What  is  the  latent  heat  of  liquefaction  of 
ice  ? 

28.  10  Ibs.  of  zinc  were  heated  to  355°  C.  and  placed  in  an  ice 
calorimeter.     At  the  end  of  a  certain  time  the  zinc  had  cooled  to 
0°  C.,  and  it  was  found  that  4.27  Ibs.  ice  had  been  melted.     Re- 
quired the  specific  heat  of  zinc. 

29.  Taking  the  annual  rainfall  at  West  Point  as  43  inches,  re- 
quired the  amount  of  heat  set  free  among  the  clouds  that  give  rain 
to  one  square  mile  of  area  in  a  year,  by  the  simple  condensation  of 
the  vapor.     1  cu.  ft.  water  weighs  62.5  Ibs.     1  mile  =  5280  ft. 

30.  A  ball  of  sulphur  weighing  5  Ibs.  was  heated  to  its  fusing 
point,  111°  C.,  and  then  dropped  into  20  Ibs.  of  turpentine  heated 
to  150°  C.     The  resulting  temperature  was   141.2°  C.     Required 
the  latent  heat  of  sulphur.     Sp.  ht.  of  turpentine  =  0.467.     Sp.  ht. 
of  sulphur  —  0.234. 

31.  A  ball  of  sulphur  weighing  17.115  Ibs.  was  heated  to  100°  0., 
and  then  dropped  into  20  Ibs.  of  turpentine  at  150°  C.     The  result- 
ing temperature  was  123.7°  C.     Required  the  latent  heat  of  sulphur. 
Fusing  point  of  sulphur =111°  C.    Sp.  ht.  of  sulphur  liquid  =  0.2;H; 
solid  =  0.202.     Sp.  ht.  of  turpentine  =  0.467. 

32.  Given   100   Ibs.  lead  at  15°  C.     Required  the  number  o<f 

*  In  all  calorimetrical  problems  no  beat  is  supposed  to  be  lost. 


168  ELEMENTARY  LESSONS  IN  HEAT. 

thermal  units  necessary  to  melt  it.     Sp.  ht.  of  lead  =  0.03.     Melt- 
ing point  =  320°  C.     Latent  heat  of  fusion  =  5.4°  0. 

33.  Given  100  Ibs.  ice  at  0°  0.     Required  the  temperature  to 
which  150  Ibs.  of  water  must  be  heated  in  order  to  just  melt  the 
ice. 

34.  Given  5  Ibs.  ice  at  0°  0.,  and  50  Ibs.  water  at  15°  C.     Re- 
quired the  first  common  temperature  resulting  from  their  mixture. 

35.  Given  10  Ibs.  ice  at  —10°  0.,  and  40  Ibs.  water  at  50°  C. 
Required  the  first  common  temperature  resulting  from  their  mix- 
ture. 

36.  Given   10  Ibs.  steam  at  100°  C.,  and  30  Ibs.  ice  at  —  40°  F. 
Required  the  temperature  that  results  from  condensing  the  steam 
in  the  ice  ? 

37.  Given  20  Ibs.  steam  at  130°  C.,  and  100  Ibs.  ice  at  —  30°  C. 
Required  the  temperature  that  results  from  their  action  upon  each 
other. 

38.  2  Ibs.  of  water  were  cooled  12°  C.  below  the  freezing  point. 
Congelation  then  set  in.     Required  the  amount  of  ice  formed. 

39.  The  dew-point  on  a  certain  day  is  10°  C.;  the  temperature 
of  the  air  21.1°  0.     Required  the  relative  humidity.     At  tempera- 
ture 10°  C.,  maximum  pressure  =  0.375.     At  temperature  211°  C. 
maximum  pressure  =  0.721. 

40.  Given  10  cu.  in.  of  water  vapor  (saturated)  at  15.5°  C.    The 
Volume  remaining  the  same,  the  temperature  is  lowered  to  10°  C. 
Required  the  volume  and  weight  of  vapor  liquefied.     100  cu.  in. 
water  vapor  (saturated)  at  10°  C.  weigh  0.247  grs.     100  cu.  in. 
Water  vapor  (saturated)  at  15.5°  C.  weigh  0.338  grs. 

41.  Given  10  cu.  in.  of  water  vapor  (saturated)  at  10°  C.     The 
temperature   remaining   the   same,  the   volume   is   diminished  to 
9  cu.  in.     Required  the  volume  and  weight  of  vapor  liquefied.    100 
cu.  in.  water  vapor  (saturated)  at  10°  C.  weigh  0.247  grs. 

42.  Suppose  the  air  over  an  area  10  miles  square,  to  the  height 
of  J  of  a  mile,  to  be  saturated  at  the  temperature  of  70°  F.     How 
much  water  would  be  produced,  and  how  much  heat  liberated  by 
the  condensation  of  all  the  moisture  in  the  space  ?    A  cubic  foot  of 
saturated  vapor  at  70°  weighs  7.99  grs. 

43.  The  absolute  conductivities  of  wrought-iron  and  platinum 
are,  respectively,  0.2  and  0.087.      Required  their  diffusivities.     Sp. 


PROBLEMS.  169 

ht.  wrought-iron=0.1138;  sp,  gr.=7.79.   Sp.  ht.  platinum =0.032 4; 
sp.  gr.  =  21.15. 

44.  In  Joule's  Experiment  a  weight  of  25  Ibs.  was  used;  the 
distance  through  which  it  fell  was  6  feet;  the  temperature  of  the 
water  in  the  vessel  was  10°  0.  before  the  experiment,  and  11°  0. 
after  the  weight  had  been  allowed  to  fall  100  times.     The  water 
weighed  10.7914  Ibs.     Required  the  mechanical  equivalent  of  a  unit 
of  heat. 

45.  Eequired  the  amount  of  heat,  an  1  its  equivalent  in  units  of 
work,  necessary  to  convert  10  Ibs.  of  ice  at  —  40°  0.  into  steam  at 
120°  0. 

46.  How  much  heat  is  given  out  by  10  Ibs.  of  steam,  at  130°  0M 
in  cooling  and  condensing  to  water  at  15.5  0.    What  is  the 

ical  equivalent  of  this  hoat  ? 


APPENDIX  II. 
TABLES. 


TABLE   I. 

LOGARITHMS. 


Proportional  Parts. 


II 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

123 

456 

789 

10 

0000 

0043 

0086 

0128 

0170    0212 

0212 

0294 

0334 

0374 

4    8  12  17  21  25 

29  33  37 

11 

0414 

0453 

0492 

0531 

0569    0607 

06*5 

0682 

0719 

0755 

4    811151923263034 

12 

0792 

0828 

0864 

0899 

0934  i  0969 

1004 

1038 

1072 

1106 

3    710141721 

24  28  31 

13 

1139 

1173 

1206 

1239 

1271    1303 

1335 

1367 

1399 

1430 

3    6  10  13  16  19  23  26  29 

14 

1461 

1492 

1523    1553 

1584    1614 

1644 

1673 

1703 

1732 

3    6    9  12  15  18  21  24  27 

15 

rei 

1^90 

1818  !  1847 

1875  ,  1903 

1931 

1959 

1987 

2014 

3    6    8  11  14  17 

20  22  25 

16 

2041 

2068   2095  i  2122 

2148  i  2175 

2201 

2227 

2253 

2279 

3    5    8  11  13  16 

18  21  24 

17 

2304 

2330    2355 

2380 

2405    2430 

2455 

2480 

2504 

2529 

2    5    7101215172022 

18 

2553 

2577    2601 

2625 

2648    2672 

2695 

2718 

2742 

2765 

257 

9  12  14 

16  19  21 

19 

2788 

2810 

2833 

2856 

2878    2900 

2923 

2945 

2967 

2989 

247 

9  11  13  16  18  20 

2O 

3010 

3032   3054 

3075 

3096 

3118 

3139 

3160 

3181 

3201 

246 

8  11  13  15  17  19 

21 

3222 

3243    3263    3284 

3304    3324 

3345 

3365 

3385 

3404 

246 

8  10  12  14  16  18 

22 

3424 

3444  '  3464 

3483 

3502    3522 

3541 

3560 

3579 

3598 

2    4    6l  8  10  12  14  15  17 

23 

3617 

3636    3655 

3674 

3692    3711 

3729 

3747 

3766 

3784 

246 

7    9  11 

13  15  17 

24     3802 

3820    3838 

3856 

3874  :  3892 

3909 

3927 

3945 

3962 

245 

7    9  11 

12  14  16 

25 

3979 

3997  i  4014 

4031 

4048    4065 

4082 

4099 

4116 

4133 

235 

7    9  10  12  14  15 

26 

4150 

4166 

4183 

4200 

4216 

4232 

4249 

4265 

4281 

4298 

235 

7    810111315 

27 

4314 

4330 

4346 

4362 

4378 

4393 

4409 

4425 

4440 

4456 

235 

689 

11  1314 

28 

4472 

4487 

4502 

4518 

4533 

4548 

4564 

4579 

4594 

4609 

235 

689 

11  12  14 

29 

4624 

4639 

4654 

4669 

4683 

4698 

4713 

4728 

4742 

4757 

1    3    4 

6    7    811  12  13 

30 

4771 

4786 

4800 

4814 

4829 

4843 

4857 

4871 

4886 

4900 

3    4 

679 

10  11  13 

31 

4914 

4928 

4942 

4955 

4969 

4983 

4997 

5011 

5024 

5038 

3    4 

678 

10  11  12 

32 

5051 

5065 

5079    5092 

5105 

5119 

5132 

5145 

5159 

5172 

3    4 

578 

9  11  12 

33 

5185 

5198 

5211 

5224 

5237 

5250 

5263 

5276 

5289 

5302 

3    4 

568 

91012 

34: 

5315 

5328 

5340 

5353 

5366 

5378 

5391 

5403 

5416 

5428 

3    4 

568 

91011 

35 

5441 

5453 

5465 

5478 

5490 

5502 

5514 

5527 

5539 

5551 

24567 

9  1011 

36 

5563 

5575 

5587 

5599 

5611 

5623 

5635 

5647 

5658 

5670 

124567 

8  1011 

37 

5682 

5694 

5705 

5717 

5729 

5740 

5752 

5763 

5775 

5786 

123567 

8    910 

38 

5798 

5809 

5821 

5832 

5843 

5855 

5866 

5877 

5888 

5899 

123567 

8    910 

39 

5911 

5922 

5933 

5944 

5955 

5966 

5977 

5988 

5999 

6010 

123 

4    5    7 

8    910 

40 

6021 

6031 

6042 

6053 

6064 

6075 

6085 

6096 

6107 

6117 

1    2    3    i    5    6 

8    9  70 

41 

6128 

6138 

6149 

6160 

6170 

6180 

6191 

6201 

6212 

6222 

123456 

789 

42 

6232 

6243 

6253 

6263 

6274 

6284 

6294 

6304 

6314 

6325 

123456 

789 

43 

6335 

6345 

6355 

6365 

6375    6385 

6395 

6405 

6415 

6425 

123456 

789 

44  !  6435 

6444 

6454 

6464 

6474    6484 

6493 

6503 

6513 

6522 

123456 

789 

45 

6532 

6542 

6551    6561 

6571 

6580 

6590 

6599 

6609, 

6618 

123456 

789 

46 

6628 

6637 

6646    6656 

6665 

6675 

6684 

6693 

6702! 

6712 

123456 

778 

47 

6721 

6730 

6739 

6749 

6758    6767 

6776 

6785 

6794 

6803 

123455 

678 

48 

6812 

6821 

6830 

6839 

6848    6857 

6866 

6875 

6884 

6893 

123445 

678 

49     6902 

6911 

6920 

6928 

6937    6946 

6955 

6964 

6972 

6981 

123445 

678 

TABLES. 


171 


TABLE   I. — Continued. 
LOGARITHMS. 


Proportional  Parts. 


¥ 

O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1  23 

456 

78  9 

50 

6990 

6998 

7007 

7016 

7024 

7033 

7042 

7050 

7059 

7067 

123 

345 

678 

51 

7076 

7084 

7093 

7101 

7110 

7118 

7126 

7135 

7143 

7152 

123 

345 

678 

52 

7160 

7168 

7177 

7185 

7193 

7202 

7210 

7218 

7226 

7235 

122 

345 

6   7   7 

53 

7243 

7251 

7259 

7267 

7275 

7284 

7292 

7300 

7308 

7316 

122 

345 

667 

54 

7324 

7332 

7340 

7348 

7356 

7364 

7372 

7380 

7388 

7396 

122 

345 

667 

55 

7404 

7412 

7419 

7427 

7435 

7443 

7451 

7459 

7466 

7474 

122 

345 

567 

56 

7482 

7490 

7497 

7505 

7513 

7520 

7528 

7536 

7543 

7551 

122 

345 

567 

57 

7559 

7566 

7574 

7582 

7589 

7597 

7604 

7612 

7619 

7627 

122 

345 

5  6   7 

58 

7634 

7642 

7649 

7657 

7664 

7672 

7679 

7686 

7694 

7701 

112 

344 

567 

59 

7704 

7716 

7723 

7731 

7738 

7745 

7752 

7760 

7767 

7774 

112 

344 

567 

60 

7782 

7789 

7796 

7803 

7810 

7818 

7825 

7832 

7839 

7846 

112 

344 

566 

61 

7853 

7860 

7868 

7875 

7882 

7889 

7896 

7903 

7910 

7917 

112 

344 

566 

62 

7924 

7931 

7938 

7945 

7952 

7959 

7966 

7973 

7980 

7987 

112 

334 

566 

63 

7993 

8000 

8007 

8014 

8021 

8028 

8035 

8041 

8048 

8055 

112 

334 

556 

64 

8062 

8069 

8075 

8082 

8089 

8096 

8102 

8109 

8116 

8122 

112 

334 

556 

65 

8129 

8136 

8142 

8149 

8156 

8162 

8169 

8176 

8182 

8189 

112 

334 

556 

66 

8195 

8202 

8209 

8215 

8222 

8228 

8235 

8241 

8248 

8254 

112 

334 

556 

67 

8261 

8267 

8274 

8280 

8287 

8293 

8299 

8306 

8312 

8319 

112 

334 

556 

68 

8325 

8331 

8338 

8344 

8351 

8357 

8363 

8370 

8376 

8382 

112 

334 

456 

69 

8388 

8395 

8401 

8407 

8414 

8420 

8426 

8432 

8439 

8445 

112 

234 

456 

70 

8451 

8457 

8463 

8470 

8476 

8482 

8488 

8494 

8500 

8506 

112 

234 

456 

71 

8513 

8519 

8525 

8531 

8537 

8543 

8549 

8555 

8561 

8567 

112 

234 

455 

72 

8573 

8579 

8585 

8591 

8597 

8603 

8609 

8615 

8621 

8627 

112 

234 

455 

73 

8633 

8639 

8645 

8651 

8657 

8663 

8G69 

8675 

8681 

8686 

112 

234 

455 

74 

8692 

8698 

8704 

8710 

8716 

8722 

8727 

8733 

8739 

8745 

112 

234 

455 

75 

8751 

8756 

8762 

8768 

8774 

8779 

8785 

8791 

8797 

8802 

112 

233 

455 

76 

8808 

8814 

8820 

8825 

8831 

8837 

8842 

8848 

8854 

8859 

112 

233 

455 

77 

8865 

8871 

8876 

8882 

8887 

8893 

8899 

8904 

8910 

8915 

112 

233 

445 

78 

8921 

8927 

8932 

8938 

8943 

8949 

8954 

8960 

8965 

8971 

112 

233 

445 

79 

8976 

8982 

8987 

8993 

8998 

9004 

9009 

9015 

9020 

9025 

1   1  2 

233 

445 

80 

9031 

9036 

9042 

9047 

9053 

9058 

9063 

9069 

9074 

9079 

112 

233 

445 

81 

9085 

9090 

9096 

9101 

9106 

9112 

9117 

9122 

9128 

9133 

112 

233 

445 

82 

9138 

9143 

9149 

9154 

9159 

9165 

9170 

9175 

9180 

9186 

112 

233 

445 

83 

9191 

9196 

9201 

9206 

9212 

9217 

9222 

9227 

9232 

9238 

112 

233 

445 

84 

9243 

9248 

9253 

9258 

9263 

9269 

9274 

9279 

9284 

9289 

112 

233 

445 

85 

9294 

9299 

9304 

9309 

9315 

9320 

9325 

9330 

9335 

9340 

112 

233 

445 

86 

9345 

9350 

9355 

9360 

9365 

9370 

9375 

9380 

9385 

9390 

112 

233 

445 

87 

9395 

9400 

9405 

9410 

9415 

9420 

9425 

9430 

9435 

9440 

Oil 

223 

344 

88 

9445 

9450 

9455 

9460 

9465 

9469 

9474 

9479 

9484 

9489 

Oil 

223 

344 

89 

9494 

9499 

9504 

9509 

9513 

9518 

9523 

9528 

9533 

9538 

Oil 

223 

344 

90 

9542 

9547 

9552 

9557 

9562 

9566 

9571 

9576 

9581 

9586 

Oil 

223 

344 

91 

9590 

9595 

9600 

9605 

9609 

9614 

9619 

9624 

9628 

9633 

0  1   1 

223 

344 

02 

9638 

9643 

9647 

9652 

9657 

9661 

9666 

9671 

9675 

9680 

Oil 

223 

344 

93 

9685 

9689 

9694 

9699 

9703 

9708 

9713 

9717 

9722 

9727 

Oil 

223 

344 

94 

9731 

9736 

9741 

9745 

9750 

9754 

9759 

9763 

9768 

9773 

Oil 

223 

344 

95 

9777 

9782 

9786 

9791 

9795 

9800 

9805 

9809 

9814 

9818 

Oil 

223 

344 

96 

9823 

9827 

9832 

9836 

9841 

9845 

9850 

9854 

9859 

9863 

Oil 

223 

344 

97 

9868 

9872 

9877 

9881 

9886 

9890 

9894 

9899 

9903 

9908 

Oil 

223 

344 

98 

9912 

9917 

9921 

9926 

9930 

9934 

9939 

9943 

9948 

9952 

Oil 

223 

344 

99 

9956 

9961 

9965 

9969 

9974 

9978 

9983 

9987 

9991 

9996 

Oil 

223 

334 

172 


ELEMENTARY  LESSONS  IN  HEAT. 


TABLE  II. 
SQUARE  ROOTS. 


n       |/n 

n       \fn 

n      V« 

n     Vn 

1 

1.0000 

26 

5.0990 

51 

7.1414 

76 

8.7178 

2 

1.4142 

27 

5.1962 

52 

7.2111 

77 

8.7750 

3 

1.7321 

28 

5.2915 

53 

7.2801 

78 

8.8318 

4 

2.0000 

29 

5.3852 

54 

7.3485 

79 

8.b882 

5 

2.2361 

30 

5.4772 

55 

7.4162 

80 

8.9443 

6 

2.4495 

31 

5.5678 

56 

7.4833 

81 

9.0000 

7 

2.6458 

32 

5.6569 

57 

7.5498 

83 

9.0554 

8 

2.8284 

33 

5.7446 

58 

7.6158 

83 

9.1104 

9 

3.0000 

34 

5.8310 

59 

7.6811 

84 

9  1652 

10 

3.1623 

35 

5.9161 

60 

7.7460 

'  85 

9.2195 

11 

3.3166 

36 

6.0UOO 

61 

7.8102 

86 

9.2736 

12 

3.4641 

37 

6.0828 

62 

7.8740 

87 

9.3274 

13 

3.6056 

38 

6.1644 

63 

7.9373 

88 

9.3808 

14 

3.7417 

39 

6.2450 

64 

8.0000 

89 

9.4340 

15 

3.8730 

40 

6.3246 

65 

8.0623 

90 

9.4868 

16 

4.0000 

41 

6.4031 

66 

8.1240 

91 

9.5394 

17 

4.1231 

42 

6.4807 

67 

8.1854 

92 

9.5917 

18 

4.2426 

43 

6.5574 

68 

8.2462 

93 

9.6437 

19 

4.3589 

44 

6.6332 

69 

8.3066 

94 

9.6954 

20 

4.4721 

45 

6.7082 

70 

8.3066 

95 

9.7468 

21 

4.5826 

46 

6.7823 

71 

8.4261 

96 

9.7980 

22 

4.6904 

47 

6.8557 

72 

8.4853 

97 

9.8489 

23 

4.7958 

48 

6.9282 

73 

8.5440 

98 

9.8995 

24 

4.8990 

49 

7.0000 

74 

8.6023 

99 

9.9499 

25 

5.0000 

50 

7.0711 

75 

8.6603 

100 

10.0000 

TABLES. 


173 


TABLE  III. 
EQUIVALENT^  THERMOMETER  READINGS. 


F. 

c. 

R. 

F. 

C. 

R. 

EG  U&1  Differences  of 

0 

-171 

-14f 

284 

140 

112 

Temperature. 

—  4 

—  20 

—  16 

000 

14^ 

1  1fi 

+  5 

™~  &\J 

-  15 

—  1U 

-  12 

*o*/O 

302 

J  7T»J 

150 

J.  1  U 

120 

A  F 

AC 

A-R 

-1-14 

-10 

-  8 

311 

155 

124 

_____ 



—  —-  —  -» 

+  23 

-  5 

-  4 

320 

160 

128 

+  82 

0 

0 

329 

165 

132 

1 

.50 

.44 

2 

1.11 

.89 

41 

+  5 

+  4 

338 

170 

136 

3 

1.67 

1.33 

50 

10 

8 

347 

175 

140 

59 

15 

12 

356 

180 

144 

4 

2.23 

1.78 

5 

2.78 

2.22 

68 

20 

16 

365 

185 

148 

6 

3.33 

2.67 

77 

25 

20 

374 

190 

152 

86 

30 

24 

383 

195 

156 

7 

3.89 

3.11 

8 

4.44 

3.56 

95 

35 

28 

392 

200 

160 

9 

5.00 

4.00 

104 

40 

32 

401 

205 

164 

113 

45 

36 

410 

210 

168 

123 

50 

40 

419 

215 

172 

AC 

AY 

AE, 

131 

55 

44 

428 

220 

176 

140 

60 

48 

437 

225 

180 

149 

65 

52 

446 

230 

184 

1 
2 

1.8 
3  6 

.8 
1.6 

158 

70 

56 

455 

235 

188 

3 

5.4 

2.4 

167 

75 

60 

464 

240 

192 

4 

7  2 

3.2 

176 

80 

64 

473 

245 

196 

5 

9.0 

40 

185 

85 

68 

482 

250 

200 

194 

90 

72 

491 

255 

204 

203 

212 

95 

100 

76 
80 

500 
509 

260 
265 

208 
212 

AR 

AC 

AF 

221 

105 

84 

518 

270 

216 





.  

230 

110 

88 

527 

275 

220 

1 

1.25 

2.25 

239 

115 

92 

536 

280 

224 

2 

2.50 

4.50 

248 

120 

96 

545 

285 

228 

3 

3  75 

675 

257 

125 

100 

554 

290 

232 

4 

5.00 

y.oo 

266 

130 

104 

563 

295 

236 

275 

135 

108 

572  I  300 

240 

174:  ELEMENTARY  LESSONS  IN  HEAT. 

TABLE  IY. 

MELTING-POINTS. 

Melting-point. 
Degrees  C. 

Aluminum 625 

Antimony 440 

Bismuth 268 

Cadmium 320 

Cobalt 1500 

Copper 1050 

Gold 1050-1065 

Iron,  cast 1050-1200 

"     steel 1300-1400 

"     wrought 1400-1 600 

Lead 325 

Magnesium 700-800 

Mercury  ........ —  40 

Nickel 1600 

Phosphorus 44 

Potassium » 62.5 

Platinum 1770 

Silver 945 

Sodium 96 

Sulphur 115 

Tin 227 

Zinc..  ...    415 


TABLES. 


175 


TABLE  Y. 

BAROMETRIC  READINGS. 
(To  pass  from  Inches  to  Millimeters,  and  vice  versa.) 


Inches. 

Mm. 

Inches. 

Mm. 

Equivalent  Lengths. 

Mm. 

Inch. 

28.0 
28.1 
28.2 
28.3 
28.4 

28.5 
28.6 
28.7 
28.8 
28.9 

29.0 
29.1 
29.2 
29.3 
29.4 

29.5 
29.6 
29.7 
29.8 
29.9 

30.0 
30.1 
30.2 
30.3 
30.4 

711.19 
713  73 
716.27 
718.81 
721.35 

723.89 
726.43 
728.97 
731.51 
734.05 

736.59 
739.13 
741.67 
744.21 
746.75 

749.29 
751.83 
754.37 
756.91 
759.45 

761.99 
764.53 
767  07 
769.61 
772.15 

30.5 
30.6 
30.7 
30.8 
30.9 

31.0 

774.69 
777.23 
779.77 
782.31 
784  85 

787.39 

.1 

.2 
.3 

.4 

.5 

.6 

.7 
.8 
.9 

1.0 
1.1 
1.2 
1.3 
1.4 

1.5 
1.6 
1.7 
1.8 
1.9 

2.0 
2.1 
2.2 
2.3 
2.4 

2.5 

.0039 
.0079 
.0118 
.0157 

.0197 
.0236 
.0276 
.0315 
.0354 

.0394 
.0433 
.0472 
.0512 
.0551 

.0591 
.0630 
.0669 
.0709 
.0748 

.0787 
.0827 
.0866 
.0906 
.0945 

.0984 

Equivalent  Lengths. 

Inch. 

Mm. 

.01 
.02 
.03 
.04 

.05 
.06 
.07 
.08 
.09 

.254 
.508 
.762 
1.016 

1.270 
1.524 
1.778 
2.032 
2.286 

176 


ELEMENTARY  LESSONS  IN  HEAT. 


TABLE  YI. 
DEW-POINT  AND  RELATIVE  HUMIDITY. 


"0*8  rf 

SB-sf 
S:=3« 

i**g 

i 

2 
3 
4 
6 
8 
10 
12 
14' 
16 
18 
20 
22 
24 

Temperature  of  Air—  Fahrenheit. 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

100° 

-7 
71 

-18 
42 

-39 
13 

5 

80 

-1 
60 

-9 

41 

-22 

21 

16 

86 

12 
72 

7 
58 

1 

44 

-18 
16 

27 
90 

24 
79 

21 

68 

17 

58 

7 
38 

-8 
18 

38 
92 

35 

84 

33 
76 

30 
68 

24 
52 

16 
37 

4 
22 

-16 

8 

48 
93 

46 

87 

44 
80 

42 

.74 

37 
61 

31 
49 

25 

37 

17 
26 

5 
16 

-20 
5 

58 
94 

57 
89 

55 

84 

53 

78 

49 
68 

45 

58 

40 

48 

35 
39 

28 
30 

20 

21 

8 
13 

-13 
5 

69 
95 

67 
90 

06 

86 

64 
81 

61 

72 

57 
64 

53 
55 

49 

48 

45 
40 

39 
33 

33 
26 

25 
19 

15 
12 

0 
6 

79 
96 

77 
92 

76 

87 

74 
83 

72 
75 

68 
68 

Co 

61 

62 

54 

58 
47 

54 

41 

50 
35 

45 

29 

39 
23 

32 

18 

89 
96 

87 
92 

86 
88 

85 

85 

82 
78 

79 
71 

77 
65 

74 
59 

70 
53 

67 
47 

63 

41 

60 
36 

56 
32 

51 
26 

99 
97 

98 
93 

96 
90 

95 

86 

93 

80 

90 

74 

87 
68 

85 
62 

82 
57 

79 

51 

76 
47 

73 

42 

69 
37 

66 
33 

Dew-point 
Kel.  humidity 

D.  P. 

R.  H. 

D.  P. 

li.  H. 

D.  P. 

R.  H. 

D.  P. 
R.  H. 

D.  P. 
R.  H. 

D.  P. 

R.  H. 

D.  P. 
R.  H. 

D.  P. 
R.  H. 

D.  P. 
R.  H. 

D.  P. 
R.  H. 

D.  P. 

R.  H. 

D.P. 
R.  H. 

D.P. 
R.  H. 

• 

NOTE. — To  obtain  reliable  results  from  the  use  of  the  psychrometer  it  is  necessary  to 
have  a  standard  rate  of  air-movement  past  the  instrument.  This  motion  maybe  accom- 
plished by  attaching  a  string  to  the  frame  of  the  two  thermometers,  when  they  are  prop- 
erly mounted,  and  whirling  them  through  the  air  for  a  couple  of  minutes  at  a  velocity  of 
twelve  or  fifteen  feet  per  second.  The  above  data  are  extracted  from  Hazen  s  table  for  use 
with  the  "  sling  "  psychrometer. 


TABLES. 


177 


TABLE  YII. 

MAXIMUM  PRESSURE  (TENSION)  OF  WATER- VAPOR  BETWEEN 
-  20°  AND  100°  C.  IN  MILLIMETERS  OF  MERCURY. 


Temper- 
ature, 
Deg.  C. 

Millimeters. 

Temper- 
ature, 
Deg.  C. 

Millimeters. 

Temper- 
ature, 
Deg.  C. 

Millimeters. 

-  20 

.907 

21 

18.4659 

62 

163.2889 

-  19 

1.0288 

22 

19.6297 

63 

170.9236 

-  18 

1.1202 

23 

20.8576 

64 

178.8585 

-  17 

1.2187 

24 

22.1524 

65 

187.1028 

-  16 

1.3248 

25 

23.5174 

66 

195.6663 

-  15 

.4390 

26 

24.9556 

67 

204.5586 

-  14 

.5618 

27 

26.4705 

68 

213.7895 

-  13 

.6939 

28 

28.0654 

69 

223.3691 

-  12 

.8357 

29 

29.7439 

70 

233.3079 

-  11 

.9880 

30 

31.5096 

71 

243.6163 

-  10 

2.1514 

31 

33.3664 

72 

254.3048 

-    9 

2.3266 

32 

35.3181 

73 

265.3849 

-    8 

2.5143 

33 

37.3689 

74 

276.8675 

-    7 

2.7153 

34 

39.5228 

75 

288.7640 

-    6 

2.9304 

35 

41.7842 

76 

301.0860 

-    5 

3.1605 

36 

44.1577 

77 

313.8475 

-    4 

3.4065 

37 

46,6477 

78 

327.0549 

-    3 

3.6693 

38 

49.2950 

79 

340.7265 

-    2 

3.9499 

39 

51.9965 

80 

354.8730 

-    1 

4.2493 

40 

54.8651 

81 

369.5075 

0 

4.5687 

41 

57.8700 

82 

384.6432 

+    1 

4.9091 

42 

61.0167 

83 

400.2933 

2 

5.2719 

43 

64.3104 

84 

416.4721 

3 

5.6582 

44 

67.7568 

85 

433.1938 

4 

6.0693 

45 

71.3619 

86 

450,4730 

5 

6.5067 

46 

75.1314 

87 

468.3240 

6 

6.9718 

47 

79.0714 

88 

486.7635 

7 

7.4660 

48 

83.1883 

89 

505.8059 

8 

7.9909 

49 

87.4882 

90 

525.4676 

9 

8.5484 

50 

91.9780 

91 

545.7650 

10 

9.1398 

51 

96.6644 

92 

566.7149 

11 

9.7671 

52 

101.5541 

93 

588.3349 

12 

10.4322 

53 

106.6546 

94 

610.6426 

13 

11.1370 

54 

111.9730 

95 

633.6567 

14 

11.8835 

55 

117.5162 

96 

657.3956 

15 

12.6739 

56 

123.2925 

97 

681.8791 

16 

13.5103 

57 

129.3095 

98 

707.1271 

17 

14.3950 

58 

135.5750 

99 

733.1602 

18 

15.3304 

59 

142.0973 

100 

760.0000 

19 

16.3189 

60 

148.8848 

20 

17.3632 

61 

155.9456 

178 


ELEMENTARY  LESSONS  IN  HEAT. 


TABLE  VIII. 

PRESSURE   OF  SATURATED   STEAM    AT    DIFFERENT  TEMPER- 
ATURES IN  POUNDS  PER  SQUARE  INCH   AT  SEA-LEVEL. 


Tempera- 
ture, 
Deg.  F. 

Pressure 
per 
Square 
Inch, 
Pounds. 

Tempera- 
ture. 
Deg.  F. 

Pressure 
per 
Square 
Inch, 
Pounds. 

Tempera- 
ture. 
Deg.  F. 

Pressure 
per 
Square 
Inch, 
Pounds. 

Tempera- 
ture, 
Deg.  F. 

Pressure 
per 
Square 
Inch, 
Pounds. 

100 

.942 

144 

3.188 

188 

8.94 

232 

21  59 

101 

.971 

145 

3.270 

189 

9.13 

233 

21  99 

102 

1.001 

146 

3.354 

190 

9.33 

234 

22.40 

103 

1.031 

147 

3.440 

191 

9.53 

235 

2282 

104 

1.062 

148 

3.527 

192 

9.74 

236 

23.25 

105 

1.094 

149 

3.616 

193 

9.95 

237 

23.67 

106 

1.127 

150 

3.707 

194 

10.16 

238 

24.11 

107 

1.160 

151 

3.800 

195 

10.38 

239 

24.55 

108 

1.195 

152 

3.895 

196 

10.60 

240 

25.00 

109 

1.230 

153 

3.992 

197 

10.82 

241 

25.46 

110 

1.267 

154 

4.091 

198 

11.05 

242 

25.92 

111 

1.304 

155 

4.192 

199 

11.29 

243 

26.39 

112 

1.342 

156 

4.295 

200 

11.52 

244 

2687 

113 

1.381 

157 

4.401 

201 

11.76 

245 

27.35 

114 

1.421 

158 

4.508 

202 

12.01 

246 

2784 

115 

1.462 

159 

4.618 

203 

12.26 

247 

28.34 

116 

1.504 

160 

4.730 

204 

12.51 

248 

28.85 

117 

1.547 

161 

4.844 

205 

12.77 

249 

29.36 

118 

1.591 

162 

4.961 

206 

1303 

250 

29.88 

119 

1.637 

163 

5.080 

207 

13.30 

251 

30.41 

120 

1.683 

164 

5.20 

208 

13.57 

252 

3094 

121 

1.781 

165 

5.32 

209 

13.84 

253 

31.48 

122 

1.779 

166 

5.45 

210 

14.12 

254 

32.03 

123 

1.829 

167 

5.58 

211 

14.41 

255 

32.59 

124 

1.880 

168 

5.71 

212 

14.70 

256 

33.15 

125 

1.932 

169 

5.85 

213 

14.99 

257 

33.73 

126 

1.985 

170 

5.98 

214 

15.29 

258 

34.31 

127 

2.040 

171 

6.12 

215 

15.60 

259 

34.90 

128 

2.096 

172 

6.26 

216 

15.91 

260 

35.50 

129 

2.154 

173 

6.40 

217 

1622 

261 

36  11 

130 

2.212 

174 

6.55 

218 

16.54 

262 

36.72 

131 

2.273 

175 

6.70 

219 

16.87 

263 

37.35 

132 

2.334 

176 

6.85 

220 

17.20 

264 

37.98 

133 

2.397 

177 

7.01 

221 

17.53 

265 

38.62 

134 

2.461 

178 

7.17 

222 

17.87 

266 

39.27 

135 

2.526 

179 

7.34 

223 

18.22 

267 

39.93 

136 

2.594 

180 

7.50 

224 

18.57 

268 

40.60 

137 

2.663 

181 

7.67 

225 

18.93 

269 

41.27 

138 

2.733 

182 

7.84 

226 

19.29 

270 

41.96 

139 

2.805 

183 

8.01 

227 

19.66 

271 

42.65 

240 

2.878 

184 

8.19 

228 

20.03 

272 

43.35 

141 

2.953 

185 

8.37 

229 

20.41 

273 

44.07 

142 

3.030 

186 

8.56 

230 

20.80 

274 

44.79 

143 

3.108 

187 

8.75 

231 

21.19 

275 

45.53 

TABLES. 


179 


TABLE  VIII. — Continued. 

PRESSURE   OF  SATURATED   STEAM    AT  DIFFERENT  TEMPER- 
ATURES  IN  POUNDS   PER   SQUARE  INCH   AT  SEA-LEVEL. 


Pressure 

Pressure 

Pressure 

Pressure 

Tempera- 

per 

Tempera- 

pei- 

Tempera- 

per 

Tempera- 

per 

ture, 

Square 

ture, 

Square 

ture, 

Square 

ture, 

Square 

Deg.  F. 

Inch, 

Deg.  F. 

Inch, 

Deg.  F. 

Inch, 

Deg.  F. 

Inch, 

Pounds. 

Pounds. 

Pounds. 

Pounds. 

276 

46.27 

308 

75.69 

[. 
340 

118.43 

372 

178.23 

277 

47.02 

309 

76.81 

341 

120.02 

373 

180.42 

278- 

47.78 

310 

77.94 

342 

121.63 

374 

182.63 

279 

48.55 

811 

79.08 

343 

1^3.26 

375 

184.86 

280 

49.33 

312 

80.23 

344 

124.89 

376 

187.11 

281 

50.13 

313 

81.40 

345 

126.55 

377 

189.38 

282 

50.93 

314 

82.59 

346 

1-38.23 

378 

191.67 

283 

51.74 

315 

83.78 

347 

129.93 

379 

193.98 

284 

52.56 

316 

84.99 

348 

131.64 

380 

196.32 

285 

53.39 

317 

86.21 

349 

133.37 

381 

198.68 

286 

54.24 

318 

87.45 

350 

135.11 

382 

201.06 

287 

55.09 

319 

88.70 

351 

136.87 

383 

203.46 

288 

55.96 

320 

89.97 

352 

138.65 

384 

205.88 

289 

56.83 

321 

91.25 

353 

140.45 

385 

208.33 

290 

57.72 

322 

9-3.54 

354 

142.27 

386 

210.79 

291 

58.62 

323 

93.85 

355 

144.10 

387 

213.28 

292 

59.53 

324 

95.17 

356 

145.95 

388 

215.79 

293 

60.45 

325 

96.51 

357 

147.82 

389 

218.32 

294 

61.38 

326 

97.86 

358 

149.72 

390 

220  .  88 

295 

62.33 

327 

99.23 

359 

151.63 

391 

223.46 

296 

63.29 

328 

100.62 

360 

153.56 

392 

226.07 

297 

64.25 

329 

102.02 

361 

155.51 

393 

228.70 

298 

65.23 

330 

103.43 

362 

157.48 

394 

231.35 

299 

66.22 

331 

104.86 

363 

159.46 

395 

234.02 

300 

67.22 

332 

106.31 

364 

161.47 

396 

236.72 

301 

68.24 

333 

107.77 

365 

163.49 

397 

239.44 

302 

69.27 

334 

109.25 

366 

165.53 

398 

242.19 

303 

70.31 

335 

110.74 

367 

167.60 

399 

244.96 

304 

71.36 

336 

112.24 

368 

169.69 

400 

247.75 

305 

72.42 

337 

113.76 

369 

171.79 

306 

73.50 

338 

115.30 

370 

173.92 

307 

74.59 

339 

116.86 

371 

176.07 

180  ELEMENTARY  LESSONS  IN  HEAT. 

TABLE  IX. 
WEIGHTS  AND  MEASURES. 

ENGLISH. 

480.0  grains  Troy  =  1  oz.  Troy. 

437.5  "  =1  oz.  Avoirdupois. 

7000.0  «  =1  Ib.  Avoirdupois. 

5760.0  "  =1  Ib.  Troy. 


The  imperial  gallon  contains  of  water  at  60°  (15°. 5  C.)  70,000  grains. 

The  pint  (£  of  a  gallon) 8,750       " 

The  fluid-ounce  (^  of  a  pint) 437.5  ' ' 

The  pint  equals  34.66  cubic  inches. 


TABLES. 


181 


gj 

fc  ^ 


w   « 

^ 

fc 

I 

I 

p 


II 


O  CO  O?  rH  CO  00  CCJ  ^ 
O  O  1O  O?  TH  CO  OO  O? 
O  O  O  CO  C3  ^  *'  °° 

oooooocbw 


00  C^  CO  IO  IO  ^^  <O  Q^ 
CO  GO  T-t  CO  'O  1C  O  O 
•"^COOOi— iCO»O»OO  -j 

IglliSaBS  £-| 

s^g  II 

,^ 


O 
CO  OJ  CO 

cog, 


•—  iGOOS 


ll 
Js 
11 

8-e 

i- 

«*j 


ill 


III! 


" 


182 


ELEMENTARY  LESSONS  IN  HEAT. 


M 

a 


K  * 
MH 


KT^      r 

II 

«5 
B  S 

£OQ 


5  K 

V]    ^1 

Jri  k^ 

PH  g 

^  2 

H   02 
EH 

S 

m 
fc 


OS  1C  C3 

Tf<30      CD  IOOSTJ<      OS      TH 

0  i-l  WCVJrH^ 

1          1          1      1       1          1 


:  : 

: 

• 

3  i  : 

: 

!  i  : 

>-»  • 

3  *  •§ 

1 

ii 

fe     r+        ' 

j*°  : 

gS^ 

8 

• 

o' 

i,     G    1 

A  •  ' 

O  «  JH 

feS  2 

ss  fl  il 


as 


i—  (O5     OO     C?  i—  1      T-I 


cc   co   cc         to  cc  w 

^  >^  §D  fcfl  §3  >^  bJD^  ^  bC  £ 


OS  1O      >O  O5 

50^5      ^      T-Ji^O      -r-t 

OT-H     O     T—  lOO     i—  i 


-^"^      »O      1CCO      T-H 
OO     O     i—  i  O     O 


- 


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1  III  1  1  j 


11 


-a 


j              ; 

:     : 

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:  :     : 

i 

; 

. 

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.  . 

0 

iiii 

1  J 

®*c  •  ' 

5t3  *  * 
^^•3  he 

^  s 

c 

1 

G 

TABLES. 


183 


i  IO  GO 
'  t-00 
i  OOOU 


TJJ  »O  i-t  W  1-1  CO  CJ  O5  1C        C3        00        IO        O  O 

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C*         j-t  CO  O         <M  «D  CO  W  r-l  r->  7-1  <M         CJ  CO  T-I         1-1  »-i  T-I  W  C^J         CO  T-I  Tp  O 
I      I      I      I      I  I      I      I      I      I      I      I      I      I      I      I      I      I  I      I      I      I      I      I      I      I      I 


S  o  *  o  „ 
-2  -£i  n^  ^  is 
'  ^-  ~  "5 


>J3  «    "3 

ife  I  -^ 

fl    <D  *5 


HPIlllig 


^   sO  T— »  ' 

>  QO  QO  GO  QO  £"•  t>*  QO  QD  !>•  GD  CD  J>*  r^-  Qfi 
lOOOOGOOOOOQOOOOOOOOOOCOOODOO 


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184 


ELEMENTARY  LESSONS  IN  HEAT. 


TABLE  XI. 

HEAVIEST    MONTHLY   RAINFALLS    EVER    RECORDED  IN  THE 
VARIOUS    STATES.* 


State. 

Station. 

Month. 

Year. 

Rainfall 
in  Inches. 

Opelika  

July.  . 

1887 

20  13 

Arizona    ...      ........ 

Camp  Goodwin       . 

August 

1880 

14  45 

Lead  Hill  

October.  .  .  . 

1883 

18  11 

January  .  .  . 

1888 

41  60 

Trinidad  

1878 

12.83 

Canton  

May.. 

1868 

18.00 

Dakota  

Webster  

Julv 

1884 

14  65 

Delaware         

Fort  Delaware  

September  .  . 

1868 

19  85 

District  of  Columbia.  .  . 
Florida         

Washington  
Ft   Barrancas 

July  
August        . 

1886 
1878 

10.63 
30  73 

Georgia  .  .  .   

Raburn  Gap     

October.  ... 

1877 

19  40 

Idaho       

Lewiston  

June      .... 

1884 

5  63 

Illinois  

Cairo  

January  .... 

1876 

15  05 

Indianapolis  

July.. 

1875 

13.12 

Fort  Gibson  

July  

1875 

11.89 

Rockford  

"          •> 

June  

1885 

18.70 

Kansas        .       ....    ... 

Elk  Falls     

April  .... 

1885 

19  00 

Louisville  

July  . 

1875 

16.46 

Alexandria  

.    *  
June  

1886 

36.91 

Eastport  

May  

1881 

13.22 

St.  John's  Church  

May  

1881 

12.30 

Amherst  

July.. 

1874 

12.61 

Northport  

May.. 

1884 

19.85 

Sylvan  Park  

July  

1872 

21.86 

1874 

23.80 

St   Louis         .  .     .   . 

June  .... 

1848 

17.07 

Fort  Ellis  

June  

1885 

12.26 

Nebraska    

Table  Rock   

June  

1883 

17.07 

Nevada...           

Fort  McDerm.it  

1883 

13.00 

Mt.  Washington  

July  

1884 

23.90 

New  Jersey              . 

August.  . 

1843 

22.50 

New  Mexico         .    .... 

Fort  Union  

August/  

1886 

8.04 

New  York  

Troy.  . 

October  

1869 

13.80 

August  

1887 

28.65 

Ohio  

Carthagena  

June  

1877 

17.33 

Oregon                     ...» 

Astoria  

January  

1880 

29.80 

Pennsylvania  ....        . 

Wellsboro  

August  

1885 

15.25 

Rhode  Island 

Block  Island  

1881 

12.93 

South  Carolina 

Charleston.  ...      ..... 

August  

1885 

19.18 

White  

July  

1883 

28.11 

Texas         

Brownsville  

September  .  .  . 

1886 

30.57 

Utah        

Mt.  Carmel  

March  

1877 

10.00 

Vermont 

Craftsburg    

October  

1869 

10.72 

Virginia 

Cape  Henry  

August  

1887 

16.82 

"\Vashington     . 

Neah  Bay..  

December  .  .  . 

1886 

30.70 

West  Virginia  

1882 

12.60 

Wisconsin  

Neillsville  

September  .  .  . 

1881 

14.01 

"Wyoming 

Hat  Creek         

April  

1879 

6.93 

*  From  Gen.  Greely's  "  American  Weather." 


INDEX. 


Absolute  temperature 105 

Air  thermometer 11,  19 

absolute  zero  of  temper- 
ature bj 21 

weight  of 64 

Alcohol  thermometer  ....'. 8 

solidification  of 56 

Anticyclonic  motion 145-151 

Archimedes,  mirror  of 81 

Atmosphere,  general  circulation 

of 132 

stable  and  unstable  condi- 
tion of 140,  141 

temperature  of,  upwards.. .   141 

Boilers 115 

causes  of  explosion  of 116 

Boiling  or  ebullition 39 

by  cold 41 

laws  of 39 

point 41 

variations  in 42 

use  made  of 43 

Bottomley's  experiment 51 

Burning  mirror 81 

Cailletet 38 

Calorimetry 27 

Carnot's  cycle 101 

Carre's  ice-machine 56 

Chimney,  draught  of 23 


Chimney,  hygroscope. 60 

Clouds,  kinds  of 156,  157 

altitude  and  thickness  of  .  157 

bursts 154 

formation 158 

shadows 157 

Condensation  of  vapor 37 

Condensers 44,  118 

Conducting  power 74 

of  hydrogen 75 

of  gases 75 

of  water 75 

power,  determination  of. .  ..68-73 

Conduction,  stages  of 67 

Conductivity,  absolute 73 

of  solids 74 

table  of  relative 74 

Continuity  of  liquid  and  gaseous 

state 37 

Convection  of  heat  in  fluids 21 

Cryophorus,  Wollaston's 55 

Culinary  paradox 41 

Curve  of  temperature 70 

of  vapor  density 95 

Cyclone  with  cold  centre 151 

Cyclones,    convectional    theory 

of 143,  144 

Bigelow's  theory  of 145,  148 

effect«on  normal  temperature  151 

motions  in 148 

Cyclones,  paths  of 149 

185 


186 


INDEX. 


PAGE 

Cyclones,  progressive  motion  of . .  148 
Cyclonic  waves 150 

Daniell's  hygrometer 61 

Density,  curve  of  vapor 35 

Density  of  vapors  in  vacua 32 

Dew 162,  163 

Dew-point 59 

second  definition 63 

from  psychrometer 65 

Diathermancy,  or  transmission  of 

heat 83 

Diffraction-grading 80 

Diff  usivity 67 

Dilation  or  expansion 13 

Dines's  hygrometer 60 

Distillation , 44 

Doldrums 137 

Dry  regions  of  the  globe 160 

Ebullition  or  boiling 39 

laws  of 39 

Eccentric,  simple Ill 

Emissive  power 82 

table  of  relative 82 

Engine,  steam 108 

classes  of 118 

compound 114 

double-acting 109 

efficiency  of 107 

high-pressure,  invented.  108 

Newcomen's 108 

oscillating 119 

reversible,  most  efficient.  119 

thermic 100 

turbine 120 

valves  of 110 

for  expansive  working. ...  Ill 

Eraporation 32 

cold  by 54 

conditions  affecting  rapidity 

of 38 

Exchanges,  theory  of 78 

Expansion  by  heat 2 

coefficients  of 13 

force  displayed  in 15 

linear. .  14 


PAQB 

Expansion  of  gases 17 

of  liquids 16 

of  mercury  and  water 16 

of  solids 14 

Ferrel  on  general  circulation . 1 33 .  1 36 

Fireplaces 23,  24 

Fly-wheel 113 

Fogs 155 

Forbes's  conductivity  determina- 
tion   68-73 

Freezing  mixtures 54 

point.. 56 

effect  of  pressure  upon . .     51 

of  solids,  table  of 49 

Frost 163 

Gauges,  pressure 116 

Gay-Lussac 17 

General  circulation  of  atmosphere  132 
in  upper  regions.  ...   138 

direction  of  winds  in 138 

Ferrel's  view  of 133,  136 

modification  of 135 

passage-winds      137 

polar  winds 138 

trade-winds 137 

Hail 161 

Ferrel's  explanation  of 162 

Heat,  latent,  of  aqueous  vapor. . .     53 

of  expansion 53 

of  fusion,   table  of,    for 

solids 49 

determination  of. ...     48 

of  ice -. 49 

of  solution 49 

of  steam 52 

of  vaporization 51 

of  vapors,  table 52 

utilization  of 54 

radiant,  general  properties  of    77 

specific 28 

determination 29 

of  gases,  table 30,  31 

of  solids 29 

of  water. .  30 


INDEX. 


1ST 


PAGE 

Heating  by  fireplaces 23 

by  hot  air 24 

by  hot  water 21 

by  steam 56 

by  stoves 25 

Humidity,  absolute 58 

Humidity,  relative 58 

from  dew-point 63 

Hygrometer,  chemical 01 

Daniell's 61 

dew-point CO 

Dines's 60 

Kegnault's 61 

Saussure's 59 

Hygrometers,  classes  of 60 

Hypsometer 43 

Ice-machines 56 

Injector,  Giff  ard's 117 

Langley 86,  90 

Law  of  Dulong  and  Petit 87 

Laws  of  cooling 87 

Liebig's  condenser 44 

Liquefaction  of  gases 37 

Mariotte's  law 19 

Maximum    and    minimum    ther- 
mometers   8 

Metallic  thermometers 11 

Meteors,  aerial 131 

aqueous 155 

Mirror,  burning 81 

Mists 155 

Monsoons 139 

Mountain  breezes 140 

Papin's  digester 44 

Peclet's  experiments 71 

Pictet 38 

Pressure,   maximum,   of   vapors 

in  vacua 32 

of  vapors  from  boiling  liquids  40 

Psychrometer 64 

Pyrometer 12 

Radiant  heat,  general  properties 

of 77 


Radiant    heat,    selective    absorp- 
tion and  emission  of 91 

Rain,  cause  of 158,  159 

measurement  of  fall ICO 

Rainfall  of  United  States 160 

Rainless  regions 160 

Reflecting  power 80 

table  of 81 

Reflection    irregular 80 

Refraction  of  heat 80 

Retort , 44 

Safety-valves 116 

Saturated  space 33 

Sleet 161 

Snow 161 

Solar  constant 86 

Solidification 50 

change  of  volume  in 51 

Spectra,  light  and  heat 79 

normal,  solar 79,  80 

maximum  heat  in 80 

Spheroidal  state 46. 

to  freeze  mercury. ......    4ft 

Steam-engine. 108 

heating 56 

navigation,  earliest 109 

pipes,  noise  of 57 

ports lift 

Still 44 

Storms 142 

low-area 151 

Superheated  vapors 34 

Temperature,  critical 37 

effect  of  altitude  upon 130 

of  a  place,  how  obtained.. .  130 

Thermal  capacity 28 

Thermo-dynamics,  first  law  of. ..  99 

second  law  of 100 

Thermometer,  construction  of. ...  4-6 

air 11,20 

alcohol... 8 

metallic 11 

Negretti's 10 

Phillips's 10 

Rutherford's 9 


188 


INDEX. 


PAGE 

Thermometer  scales 6 

Six's 8 

Thermopile 80 

Tornadoes 152 

Transmission  of  heat,  diather- 
mancy       83 

effect  of  source  upon  ...     84 
influence     of     medium 

upon 84 

of  sun's  heat  through  earth's 

atmosphere 86 

Turbine  engine,  action  of 121 

of  Curtis 123 

definition 120 

of  De  Laval....   121 

earliest 120 

efficiency  of....  122 
Ocean  going  ...  129 
of  Parsons 128 

Unit  of  heat..  27 


Unit  of  heat,  mechanical  equiva- 
lent of,  Joule's 97,  98 

Rowland's     determina- 
tions    98 

Vapor,  weight  of,  in  saturated 

space 35 

Vaporization 32 

Ventilation 26 

Water-spouts 153 

Watt's  improvements  of  engine.  108 

Whirlwinds 141 

Winds,  local,  periodic 139 

of  the  general  circulation. .  133 

of  polar  regions 138 

of  temperate  regions 137 

passage 137 

system  of 137 

trade 137 

veering  of 149 


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7 


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